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@article{THSP_2008_14_2_a4, author = {Alexander B. Kharazishvili}, title = {On a bad descriptive structure of {Minkowski{\textquoteright}s} sum}, journal = {Teori\^a slu\v{c}ajnyh processov}, pages = {35--41}, publisher = {mathdoc}, volume = {14}, number = {2}, year = {2008}, language = {en}, url = {http://geodesic.mathdoc.fr/item/THSP_2008_14_2_a4/} }
Alexander B. Kharazishvili. On a bad descriptive structure of Minkowski’s sum. Teoriâ slučajnyh processov, Tome 14 (2008) no. 2, pp. 35-41. http://geodesic.mathdoc.fr/item/THSP_2008_14_2_a4/
[1] B. R. Gelbaum, J. M. H. Olmsted, Counterexamples in Analysis, Holden Day, San Francisco, 1964 | MR | Zbl
[2] J. C. Morgan II, Point Set Theory, Marcel Dekker, New York, 1990 | MR | Zbl
[3] B. S. Sodnomov, “On arithmetical sums of sets”, Dokl. Akad. Nauk SSSR, 80 (1951), 173–175 (in Russian) | MR | Zbl
[4] B. S. Sodnomov, “An example of two $G_\delta$-sets, whose arithmetical sum is not Borel measurable”, Dokl. Akad. Nauk SSSR, 99 (1954), 507–510 (in Russian) | MR | Zbl
[5] P. Erdös, A. H. Stone, “On the sum of two Borel sets”, Proc. Amer. Math. Soc., 25:2 (1970), 304–306 | DOI | MR | Zbl
[6] C. A. Rogers, “A linear Borel set whose difference set is not a Borel set”, Bull. London Math. Soc., 2 (1970), 41–42 | DOI | MR | Zbl
[7] J. Cichoń, A. Jasiński, “A note on algebraic sums of subsets of the real line”, Real Analysis Exchange, 28:2 (2002-2003), 493–500 | MR
[8] W. Sierpiński, “Sur la question de la mesurabilité de la base de M.Hamel”, Fund. Math., 1 (1920), 105–111 | DOI | Zbl
[9] A. B. Kharazishvili, Applications of Point Set Theory in Real Analysis, Kluwer, Dordrecht, 1998 | MR | Zbl
[10] K. Kuratowski, Topology, v. I, Academic Press, New York, 1966 | MR | Zbl
[11] A. W. Miller, “Special subsets of the real line”, Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 201–234 | DOI | MR
[12] E. Grzegorek, “Solution of a problem of Banach on $\sigma$-fields without continuous measures”, Bull. Acad. Polon. Sci., Ser. Sci. Math., 28 (1980), 7–10 | MR | Zbl
[13] W. F. Pfeffer, K. Prikry, “Small spaces”, Proc. London Math. Soc., 58:3 (1989), 417–438 | DOI | MR | Zbl
[14] P. Zakrzewski, “On a construction of universally small sets”, Real Analysis Exchange, 28:1 (2002-2003), 221–226 | DOI | MR
[15] J. C. Oxtoby, Measure and Category, Springer, Berlin, 1971 | MR | Zbl
[16] P. Erdös, K. Kunen, R. D. Mauldin, “Some additive properties of sets of real numbers”, Fund. Math., CXIII:3 (1981), 187–199 | DOI | MR | Zbl
[17] K. Ciesielski, H. Fejzić, C. Freiling, “Measure zero sets with nonmeasurable sum”, Real Analysis Exchange, 27:2 (2001-2002), 783–794 | DOI | MR
[18] A. B. Kharazishvili, “The algebraic sum of two absolutely negligible sets can be an absolutely nonmeasurable set”, Georgian Mathematical Journal, 12:3 (2005), 455–460 | MR | Zbl
[19] A. B. Kharazishvili, A. P. Kirtadze, “On algebraic sums of measure zero sets in uncountable commutative groups”, Proc. A. Razmadze Math. Institute, 135, 2004, 97–103 | MR | Zbl
[20] A. B. Kharazishvili, A. P. Kirtadze, “On algebraic sums of absolutely negligible sets”, Proc. A. Razmadze Math. Institute, 136, 55–61 | MR | Zbl
[21] A. B. Kharazishvili, A. P. Kirtadze, “On measurability of algebraic sums of small sets”, Studia Scientiarum Mathematicarum Hungarica, 45:2 (2008), 81–90 | MR
[22] A. V. Skorokhod, Integration in Hilbert Space, Nauka, Moscow, 1974 (in Russian) | MR