# Citations

On the classification of measure zero sets, preprint (1983)

cited in:

• C. Laflamme, Some possible covers of measure zero sets , Coll. Math. 63 (1992), 211-218.
• C. Laflamme, A few sigma-ideals of measure zero sets related to their covers, Real Analysis Exchange 17(1) (1991/92), 362-370.

The existence of universal invariant semiregular measures on groups, Proc. Amer. Math. Soc. 99 (1987), 507-508.

cited in:

• M. Laczkovich, Paradoxical decompositions: a survey of recent results, in: First European Congress of Mathematics (Paris, July 6-10, 1992), Vol. II, Progr. Math., Vol. 120, Birkhauser, Basel, 159-184.
• S. Solecki, On Sets Nonmeasurable with Respect to Invariant Measures, Proceedings of the American Mathematical Society 119 (1993), 115-124.
• A. B. Kharazishvili, Nonmeasurable sets and functions, Jan van Mill, Ed., Elsevier Science B.V., 2004.

The existence of universal invariant measures on large sets, Fund. Math.133 (1989), 113-124.

cited in:

• M. Laczkovich, Paradoxical decompositions: a survey of recent results, in: First European Congress of Mathematics (Paris, July 6-10, 1992), Vol. II, Progr. Math., Vol. 120, Birkhauser, Basel, 159-184.
• A. B. Kharazishvili, Nonmeasurable sets and functions, Jan van Mill, Ed., Elsevier Science B.V., 2004.

On universal semiregular invariant measures, Journal of Symbolic Logic 53 (1988), 1170-1176.

cited in:

• M. Laczkovich, Paradoxical decompositions: a survey of recent results, in: First European Congress of Mathematics (Paris, July 6-10, 1992), Vol. II, Progr. Math., Vol. 120, Birkhauser, Basel, 159-184.

Extensions of isometrically invariant measures on Euclidean spaces, Proc. Amer. Math. Soc. 110 (1990), 325-331.

cited in:

• M. Laczkovich, Paradoxical decompositions: a survey of recent results, in: First European Congress of Mathematics (Paris, July 6-10, 1992), Vol. II, Progr. Math., Vol. 120, Birkhauser, Basel, 159-184.
• K. Ciesielski , Set Theoretic Real Analysis, J. Appl. Anal. 3(2) (1997), 143-190.
• M. Laczkovich, Paradoxes in measure theory, in: Handbook of Measure Theory, E. Pap, Ed. , Elsevier 2002, 83-123. (2002), 285-302.
• A. B. Kharazishvili, Nonmeasurable sets and functions, Jan van Mill, Ed., Elsevier Science B.V., 2004.
• A. B. Kharazishvili, Strange functions in real analysis, Chapman & Hall/CRC, 2006.
• A. B. Kharazishvili, A. Kirtadze, On nonmeasurable subgroups of uncountable solvable groups, Georgian Mathematical Journal 14(3) (2007), 435-444.
• A. B. Kharazishvili, On thick subgroups of uncountable sigma-compact locally compact commutative groups, Topology and its Applications 156 (14), 2009, 2364-2369.
• A. B. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions, Atlantis Studies in Mathematics, J. van Mill, Ed., Atlantis Press, 2009.
• A. B. Kharazishvili, Some unsolved problems in measure theory, Proceedings of A. Razmadze Mathematical Institute Vol. 162 (2013), 59–77.

Extensions of measures invariant under countable groups of transformations, Trans. Amer. Math. Soc. 326 (1991), 211-226. (with A. Krawczyk).

cited in:

• K. Ciesielski, Set Theoretic Real Analysis , J. Appl. Anal.3(2) (1997), 143-190.
• A. B. Kharazishvili, Nonmeasurable sets and functions, Jan van Mill, Ed., Elsevier Science B.V., 2004.
• A. B. Kharazishvili, A. P. Kirtadze, On Weakly Metrically Transitive Measures and Nonmeasurable Sets, Real Anal. Exchange Volume 32(2) (2006), 553-562.
• A. B. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions, Atlantis Studies in Mathematics, J. van Mill, Ed., Atlantis Press, 2009.
• P. S. Chami, N. Sookoo, Induced measures on mu**-measurable sets, Journal of Interdisciplinary Mathematics 13(6), 2010, 691-702.

Paradoxical decompositions and invariant measures, Proc. Amer. Math. Soc. 111 (1991), 533-539.

cited in:

• D. H. Fremlin, Real-valued-measurable cardinals, in: Set Theory of the Reals, H. Judah, Ed., Bar-Ilan University (1993), 151-304.
• M. Laczkovich, Paradoxical decompositions: a survey of recent results, in: First European Congress of Mathematics (Paris, July 6-10, 1992), Vol. II, Progr. Math., Vol. 120, Birkhauser, Basel, 159-184.
• M. Laczkovich, Paradoxes in measure theory, in: Handbook of Measure Theory, E. Pap, Ed. , Elsevier 2002, 83-123. (2002), 285-302.
• A. B. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions, Atlantis Studies in Mathematics, J. van Mill, Ed., Atlantis Press, 2009.
• A. Nowik, Hereditarily nonparadoxical sets revisited, Topology and its Applications, 161(2014), 377–385.
• P. Komjath, A remark on hereditarily nonparadoxical sets , Arch. for Math. Logic, 55(2016), 165–175.

When do equidecomposable sets have equal measures?, Proc. Amer. Math. Soc. 113 (1991), 831-837.

cited in:

• A. B. Kharazishvili, Nonmeasurable sets and functions, Jan van Mill, Ed., Elsevier Science B.V., 2004.
• A. B. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions, Atlantis Studies in Mathematics, J. van Mill, Ed., Atlantis Press, 2009.

Strong Fubini axioms from measure extension axioms, Comment. Math. Univ. Carolinae 33.2 (1992), 291-297.

cited in:

• R. D. Mabry, Subsets of the plane with constant linear shade, Real Analysis Exchange, 24(1) (1998/99), 35-38.
• D. H. Fremlin, Measure Theory, Vol. 5, Torres Fremlin, 2008.

The existence of invariant probability measures for a group of transformations, Israel J. Math. 83 (1993), 343-352.

cited in:

• H. Becker and A. S. Kechris, Borel actions of Polish groups, Bulletin of the American Mathematical Society, 28(2), (1993), 334-341.
• H. Becker and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, Cambridge University Press, 1996.
• M. G. Nadkarni, Basic Ergodic Theory, Birkhauser, 1998.
• M. Laczkovich, Paradoxes in measure theory, in: Handbook of Measure Theory, E. Pap, Ed. , Elsevier 2002, 83-123. (2002), 285-302.
• A. B. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions, Atlantis Studies in Mathematics, J. van Mill, Ed., Atlantis Press, 2009.

The existence of invariant sigma-finite measures for a group of transformations, Israel J. Math. 83 (1993), 275-287.

cited in:

• A. B. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions, Atlantis Studies in Mathematics, J. van Mill, Ed., Atlantis Press, 2009.
• P. Niemiec, A note on invariant measures , Opuscula Mathematica, 31(3), (2011), 425-431.

The existence of nonmeasurable sets for invariant measures, Proc. Amer. Math. Soc. 121 (1994), 579-584. (with M. Penconek)

cited in:

• W. Schindler, Measures with Symmetry Properties Springer-Verlag, 2003.

When do sets admit congruent partitions, Quart. J. Math. Oxford (2), 45 (1994), 255-265.

cited in:

• M. Laczkovich, Paradoxes in measure theory, in: Handbook of Measure Theory, E. Pap, Ed. , Elsevier 2002, 83-123. (2002), 285-302.
• A. B. Kharazishvili, Nonmeasurable sets and functions, Jan van Mill, Ed., Elsevier Science B.V., 2004.

Extending invariant measures on topological groups , in: The Proceedings of the Tenth Summer Conference on Topology and Applications, Annals of the New York Academy of Sciences 788 (1996), 218-222.

cited in:

• A. B. Kharazishvili, Nonmeasurable sets and functions, Jan van Mill, Ed., Elsevier Science B.V., 2004.
• R. Filipów, On the difference property of families of measurable functions, Colloq. Math. 97(2) (2003), 169-180.
• A. B. Kharazishvili, A. Kirtadze, On nonmeasurable subgroups of uncountable solvable groups, Georgian Mathematical Journal 14(3) (2007), 435-444.
• A. B. Kharazishvili, On thick subgroups of uncountable sigma-compact locally compact commutative groups, Topology and its Applications, 156(14), (2009), 2364-2369.
• A. B. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions, Atlantis Studies in Mathematics, J. van Mill, Ed., Atlantis Press, 2009.
• A. B. Kharazishvili, Some unsolved problems in measure theory, Proceedings of A. Razmadze Mathematical Institute Vol. 162 (2013), 59–77.

Extending isometrically invariant measures on R n - a solution to Ciesielski's query , Real Analysis Exchange 21 (1995/96), 582-589.

cited in:

• K. Ciesielski, Set Theoretic Real Analysis , J. Appl. Anal. 3(2) (1997), 143-190.
• M. Laczkovich, Paradoxes in measure theory, in: Handbook of Measure Theory, E. Pap, Ed. , Elsevier 2002, 83-123. (2002), 285-302.
• A. B. Kharazishvili, Nonmeasurable sets and functions, Jan van Mill, Ed., Elsevier Science B.V., 2004.

The uniqueness of Haar measure and set theory , Coll. Math. 74 (1997), 109-121. <

cited in:

• A. B. Kharazishvili, Nonmeasurable sets and functions, Jan van Mill, Ed., Elsevier Science B.V., 2004.
• A. P. Kirtadze, On the Uniqueness Property for invariant measures, Georgian Math. Journal 12(3), (2005), 475-483.
• G. Pantsulaia, Invariant and quasiinvariant neasures in infinite-dimensional topological vector spaces, Nova Science Publishers, Inc, 2007 .
• A. B. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions, Atlantis Studies in Mathematics, J. van Mill, Ed., Atlantis Press, 2009.
• A. B. Kharazishvili, Some unsolved problems in measure theory, Proceedings of A. Razmadze Mathematical Institute Vol. 162 (2013), 59–77.

Strong Fubini properties of ideals , Fund. Math. 159 (1999), 135-152. (with I. Reclaw)

cited in:

• I. Rec³aw, Fubini properties for sigma-centered sigma-ideals, preprint, http://mat.ug.edu.pl/~reclaw/publications.html.
• I. Rec³aw, On the double difference property for functions with the Baire Property, preprint, http://mat.ug.edu.pl/~reclaw/publications.html.
• R. Filipów, On the difference property of the family of functions with the Baire property, Acta Math. Hungar.100(1-2) (2003), 97-104.
• T. Natkaniec, The I-almost constant convergence of sequences of real functions, Real Analysis Exchange 28(2) (2002/2003), 481-491.
• K. Ciesielski, M. Laczkovich, Strong Fubini properties for measure and category, Fund. Math. 178(2) (2003), 171-188.
• É. Matheron and M. Zelený, Descriptive set theory of families of small sets, Bull. Symbolic Logic 13(4) (2007), 482-537.

Fubini properties of ideals , Real Analysis Exchange 25(1999/00), no.2, 565-578. (with I. Reclaw)

cited in:

• I. Rec³aw, Fubini properties for sigma-centered sigma-ideals, preprint, http://mat.ug.edu.pl/~reclaw/publications.html.
• S.Solecki, A Fubini theorem, Topology and its Applications 154 (2007), 2462-2464.
• I. Farah, J. Zapletal, Between Maharam's and von Neumann's problems, Math. Res. Lett. 11(5-6) (2004), 673-684.
• P. Borodulin-Nadzieja, Sz. G³ab, Ideals with bases of unbounded Borel complexity, Mathematical Logic Quarterly, 57 (2011), no. 6, 582-590.
• H. Becker, Cocycles and continuity , Trans. Amer. Math. Soc. 365 (2013), no. 2, 671-719.

Extending Baire Property by countably many sets , Proc. Amer. Math. Soc. 129(2001), no.1, 271-278.

cited in:

• P. Kawa, J. Pawlikowski, Extending Baire Property by uncountably many sets, Journal of Symbolic Logic 75(3) (2010), 896-904.

Universally Meager Sets , Proc. Amer. Math. Soc. 129(2001), no.6, 1793-1798.

cited in:

• A. Nowik, T. Weiss, Not every Q-set is perfectly meager in the transitive sense, Proc. Amer. Math. Soc. 128(10) (2000), 3017-3024.
• I. Rec³aw, On a construction of universally null sets, Real Analysis Exchange, 27(1) (2001/02), 321-323.
• T. Bartoszynski, S. Shelah, Perfectly meager sets and universally null sets, Proc. Amer. Math. Soc. 130(12) (2002), 3701-3711.
• T. Bartoszynski, On perfectly meager sets, Proc. Amer. Math. Soc., 130(4) (2002), 1189-1195.
• O. Zindulka, Small opaque sets, Real Analysis Exchange 28(2), 2002/2003, 455-470.
• T. Bartoszynski, Remarks on small sets of reals, Proc. Amer. Math. Soc., 131(2) (2003), 625-630.
• T. Bartoszyñski, B. Tsaban, Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures, Proc. Amer. Math. Soc., 134(2) (2006), 605-615.
• P. Elias, Permitted sets are perfectly meager in transitive sense, preprint (2007), http://ics.upjs.sk/~elias/publications/.
• B. Tsaban, L. Zdomsky, Scales, fields, and a problem of Hurewicz, J. Eur. Math. Soc. (JEMS) 10 (2008), 837-866.
• A. Nowik, P. Reardon, Uniform algebras in the Cantor and Baire space, Journal of Applied Analysis 14(2) (2008), 227-238.
• J. Kraszewski, Everywhere meagre and everywhere null sets, Houston journal of mathematics 35(1) (2009), 103-111.
• M. Sakai, Menger subsets of the Sorgenfrey line, Proc. Amer. Math. Soc. 137 (2009), 3129-3138.
• P. Elias, Dirichlet sets, Erdõs-Kunen-Mauldin theorem, and analytic subgroups of the reals, Proc. Amer. Math. Soc., (2010).
• T. Banakh, N. Lyaskovska, Constructing universally small subsets of a given packing index in Polish groups, Colloq. Math. 125 (2011), no. 2, 213–220.
• O. Zindulka, Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps, Fund. Math. 218(2) (2012), 95–119.
• O. Zindulka, Small sets of reals through the prism of fractal dimensions, Fund. Math. 218(2) (2012), 95–119.
• R. Pol, P. Zakrzewski, On Borel mappings and sigma-ideals generated by closed sets, Adv. Math. 231 (2012), no. 2, 651-663.
• M. Korch, T. Weiss, On the Class of Perfectly Null Sets and Its Transitive Version, Bulletin Polish Acad. Sci. Math. 64 (2016), 1-20.

Some set-theoretic aspects of measure theory, Cubo Matematica Educacional Vol. 3, no. 2 (2001), 75-88.

cited in:

• P.G.L. Porta Mana, A. Mansson, G. Bjork, The Laplace-Jaynes approach to induction, preprint (2007), http://arxiv.org/PS_cache/physics/pdf/0703/0703126v2.pdf.

Measures on algebraic-topological structures, Handbook of Measure Theory, ed. E. Pap, Elsevier 2002, 1091-1130.

cited in:

• M. Laczkovich, Paradoxes in measure theory, in: Handbook of Measure Theory, E. Pap, Ed. , Elsevier 2002, 83-123. (2002), 285-302.
• T. Banakh, Cardinal characteristics of the ideal of Haar null sets,Comment.Math.Univ.Carolinae 45(1) (2004), 119-137.
• P. Niemiec, Invariant measures for equicontinuous semigroups of continuous transformations of a compact Hausdorff space, Topology and its Applications 153(18) (2006), 3373-3382.
• B. D. Miller, On the existence of invariant probability measures for Borel actions of countable semigroups , preprint (2006), http://glimmeffros.googlepages.com/.
• A. B. Kharazishvili, Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions, Atlantis Studies in Mathematics, J. van Mill, Ed., Atlantis Press, 2009.
• A. B. Kharazishvili, Finite families of negligible sets and invariant extensions of the Lebesgue measure, Proc. A. Razmadze Math. Inst., vol. 151, 2009, pp. 119-123.
• A. B. Kharazishvili, A combinatorial problem on translation-invariant extensions of the Lebesgue measure, Expositiones Mathematicae 29 (2011), 150–158.
• P. Niemiec, A note on invariant measures, Opuscula Mathematica, 31(3), (2011), 425-431.
• A. B. Kharazishvili, Measurability Properties of Vitali Sets , The American Mathematical Monthly, Vol. 118, No. 8 (October 2011), pp. 693-703.
• A. B. Kharazishvili, Some unsolved problems in measure theory, Proceedings of A. Razmadze Mathematical Institute Vol. 162 (2013), 59–77.
• A. B. Kharazishvili, On Countable Almost Invariant Partitions of G-Spaces, Ukr. Math. J. Vol. 66, Issue 4 (2014), 572–579.
• A. B. Kharazishvili, On measurability properties of Bernstein sets, Proceedings of A. Razmadze Mathematical Institute, 164 (2014), 63-70.
• A. B. Kharazishvili, To the existence of projective absolutely nonmeasurable functions, Proceedings of A. Razmadze Mathematical Institute, 166 (2014), 95-102.
• A. B. Kharazishvili, Set Theoretical Aspects of Real Analysis , CRC Press Taylor & Francis Group, 2015.
• A. B. Kharazishvili, A partition of an uncountable solvable group into three negligible subsets , Bulletin of TICMI Vol. 19, No. 1 (2015), 37-44.
• A. B. Kharazishvili, On negligible and absolutely nonmeasurable subsets of uncountable solvable groups , Transactions of A. Razmadze Mathematical Institute 170 (2016), 69–74.
• A. B. Kharazishvili, On the cardinal number of the family of all invariant extensions of a nonzero sigma-finite invariant measure , Transactions of A. Razmadze Mathematical Institute, 170 (2016), 200–204.
• M. de Jeu, J. Rozendaal, Disintegration of positive isometric group representations on Lp-spaces , Positivity (2017), 673-710.

On a construction of universally small sets, Real Analysis Exchange 27(2) (2002), pp.1-6.

cited in:

• A. B. Kharazishvili, A. Razmadze, On additive absolutely nonmeasurable Sierpiñski-Zygmund functions, Real Anal. Exchange Volume 31(2) (2005), 553-560.
• A. B. Kharazishvili, Strange functions in real analysis, Chapman & Hall/CRC, 2006.
• A. B. Kharazishvili, A.P. Kirtadze, On extensions of partial functions,Expositiones Mathematicae 25(4) (2007), 345-353.
• A. B. Kharazishvili, A nonseparable extension of the Lebesgue measure without new nullsets,Real Anal. Exchange Volume 33(1) (2007), 263-274.
• A. B. Kharazishvili, On a bad descriptive structure of Minkowski's sum of certain small sets in a topological vector space, Theory of Stochastic Processes 14(30), no. 2, (2008), 35-41.
• A. B. Kharazishvili, On measurability of algebraic sums of small sets, Studia Scientiarum Mathematicarum Hungarica 45(3) (2008), 433-442 .
• A. B. Kharazishvili, On Absolutely Nonmeasurable Sets and Functions, Georgian Mathematical Journal 15(2) (2008), 317--325.
• W. Kubis, B. Vejnar, Covering an uncountable square by countably many continuous functions, Proc. Amer. Math. Soc. 140(12) (2012), 4359–4368.
• A. B. Kharazishvili, On almost measurable real-valued functions, Studia Scientiarum Mathematicarum Hungarica (2009), http://www.akademiai.com/content/c3783201716g5743/.
• O. Zindulka, Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps, Fund. Math. 218(2) (2012), 95–119.
• T. Banakh, N. Lyaskovska, Constructing universally small subsets of a given packing index in Polish groups , Colloq. Math. 125 (2011), no. 2, 213-220.
• A. B. Kharazishvili, To the existence of projective absolutely nonmeasurable functions, Proceedings of A. Razmadze Mathematical Institute, 166 (2014), 95-102.
• A. B. Kharazishvili, Set Theoretical Aspects of Real Analysis , CRC Press Taylor & Francis Group, 2015.

Fubini properties for filter--related $\sigma$-ideals, Topology and its Applications 136/1-3 (2004), 239-249.

cited in:

• S. Solecki , A Fubini theorem, Topology and its Applications 154 (2007), 2462-2464.

On the uniqueness of measure and category \sigma-ideals on 2^{\omega}, Journal of Applied Analysis 13, No. 2 (2007), 249-257.

cited in:

• P. Borodulin-Nadzieja, Sz. G³ab, Ideals with bases of unbounded Borel complexity, Mathematical Logic Quarterly, 57 (2011), no. 6, 582–590.

Universally meager sets, II, Topology and its Applications 155 (2008), 1445-1449.

cited in:

• A. Nowik, P. Reardon, Uniform algebras in the Cantor and Baire space, Journal of Applied Analysis 14(2) (2008), 227-238.
• O. Zindulka, Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps, Fund. Math. 218(2) (2012), 95–119.

On the complexity of the ideal of absolute null sets, Ukrainian Mathematical Journal, 64 (2012), no. 2, 275-276.

cited in:

• T. Banakh, The Solecki submeasures on groups, preprint, http://arxiv.org/abs/1211.0717.

On Borel mappings and sigma-ideals generated by closed sets (with R. Pol), Adv. Math. 231 (2012), no. 2, 651-663.

cited in:

• V. Kanovei, M. Sabok, J. Zapletal, Canonical Ramsey Theory on Polish Spaces , Cambridge University Press, Cambridge, 2013.
• J. Zapletal, Analytic equivalence relations and the forcing method, Bulletin of Symbolic Logic 19(4) (2013), 473-490.
• J. Zapletal, Dimension theory and forcing, Topology and its Applications 167 (2014), 31-35.
• R. Pol, Note on Borel mappings and dimension, Topology and its Applications 195 (2015), 275-283.
• R. Pol, P. Zakrzewski On Boolean algebras related to sigma-ideals generated by compact sets, Advances in Mathematics 297 (2016).
• T. Kihara, Higher randomness and lim-sup forcing within and beyond hyperarithmetic, Proceedings of the Singapore programme "Sets and Computation", 2016, to appear.
• T. Kihara, A. Pauly, Point degree spectra of represented spaces, arXiv:1405.6866v4 [math.GN].
• E. Pol, R. Pol, Isometric embeddings and continuous maps onto the irrationals, Topology and its Applications arXiv:1706.04396v1 [math.GN].
• T. Kihara, Effective forcing with Cantor manifolds, arXiv:1702.02630v1 [math.LO].
• R. Pol, P. Zakrzewski On Borel maps, calibrated sigma-ideals and homogeneity, arXiv:1706.04773v1 [math.LO] .