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

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• I. Recław, Fubini properties for sigma-centered sigma-ideals, preprint, http://mat.ug.edu.pl/~reclaw/publications.html.
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Extending Baire Property by countably many sets , Proc. Amer. Math. Soc. 129(2001), no.1, 271-278.

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

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• 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.
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• 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.
• A. B. Kharazishvili, Some remarks on the Steinhaus property for invariant extensions of the Lebesgue measure , Eur. J. Math. 5 (2019), no. 1, 81–90.

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

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• A. B. Kharazishvili, A. Razmadze, On additive absolutely nonmeasurable Sierpiński-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.
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• 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.

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• 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.

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• P. Borodulin-Nadzieja, Sz. Głab, 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.

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• 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 nonmeasurable selectors of countable group actions. Fund. Math. 202 (2009), 281-294

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• A. B. Kharazishvili, On countable almost invariant partitions of G-spaces, Ukrainian Math. J. 66 (2014), no. 4, 572–579.

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

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• 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.

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• 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.
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• T. Kihara, Effective forcing with Cantor manifolds, arXiv:1702.02630v1 [math.LO].
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• R. Pol, P. Zakrzewski On Mazurkiewicz's sets, thin ?-ideals of compact sets and the space of probability measures on the rationals, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115 (2021), no. 2, Paper No. 42, 16 pp.

On Borel sets belonging to every invariant ccc sigma-ideal on 2^omega. Proc. Amer. Math. Soc. 141 (2013), no. 3, 1055-1065.

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On invariant ccc sigma-ideals on 2^N. Acta. Math. Hungar. 143 (2) (2014), 367-377.

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• Conley, Clinton T.; Marks, Andrew S.; Tucker-Drob, Robin D., Brooks' theorem for measurable colorings, Forum Math. Sigma 4 (2016), e16, 23 pp.
• Burke, M. R.; Macheras, N. D.; Strauss, W., Products of derived structures on topological spaces, Topology Appl. 201 (2016), 247–268.

A characterization of the meager ideal. Comment. Math. Univ. Carolin. 56,1 (2015) 45–50.

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On Boolean algebras related to sigma-ideals generated by compact sets. (with R. Pol) Adv. Math. 297 (2016), 196-213.

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Combinatorics of ideals – selectivity versus density. (with A. Kwela) Comment. Math. Univ. Carolin. 58,2 (2017), 261-266.

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• M. Kwela, A. Nowik, Ideals of nowhere dense sets in some topologies on positive integers, Topology Appl. 248 (2018), 149-163.

On Borel maps, calibrated sigma-ideals and homogeneity. (with R. Pol) Trans. Amer. Math. Soc. 370 (2018), 8959-8978.

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