Measurability of functions with approximately continuous vertical sections and measurable horizontal sections

• Autorzy: M. Laczkovich , Arnold W. Miller
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 69
• Numer: 2
• Strony: 299-308

Daty

wydano

1996

otrzymano

1994-11-22

poprawiono

1995-04-04

Twórcy

autor

M. Laczkovich

• Department of Analysis, Loránd Eötvös University, Múzeum krt. 6-8, H-1088 Budapest, Hungary

autor

Arnold W. Miller

• Department of Mathematics, University of Wisconsin-Madison, Van Vleck Hall, Madison, Wisconsin 53706-1388, U.S.A

Bibliografia

• [1] T. Bartoszyński and S. Shelah, Closed measure zero sets, Ann. Pure Appl. Logic 58 (1992), 93-110.
• [2] J. Bourgain, D. H. Fremlin and M. Talagrand, Pointwise compact sets of Baire measurable functions, Amer. J. Math. 100 (1978), 845-886.
• [3] A. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. 659, Springer, 1978.
• [4] T. Carlson, Extending Lebesgue measure by infinitely many sets, Pacific J. Math. 115 (1984), 33-45.
• [5] R. O. Davies, Separate approximate continuity implies measurability, Proc. Cambridge Philos. Soc. 73 (1973), 461-465.
• [6] R. O. Davies and J. Dravecký, On the measurability of functions of two variables, Mat. Časopis 23 (1973), 285-289.
• [7] A. Denjoy, Sur les fonctions dérivées sommables, Bull. Soc. Math. France 43 (1916), 161-248.
• [8] C. Freiling, Axioms of symmetry: throwing darts at the real number line, J. Symbolic Logic 51 (1986), 190-200.
• [9] C. Goffman, C. J. Neugebauer and T. Nishiura, Density topology and approximate continuity, Duke Math. J. 28 (1961), 497-506.
• [10] Z. Grande, La mesurabilité des fonctions de deux variables, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 22 (1974), 657-661.
• [11] T. Jech, Set Theory, Academic Press, 1978.
• [12] P. Komjáth, Some remarks on second category sets, Colloq. Math. 66 (1993), 57-62.
• [13] K. Kunen, Random and Cohen reals, in: Handbook of Set-Theoretic Topology, North-Holland, 1984, 887-911.
• [14] K. Kuratowski, Topology, Vol. 1, Academic Press, 1966.
• [15] M. Laczkovich and G. Petruska, Sectionwise properties and measurability of functions of two variables, Acta Math. Acad. Sci. Hungar. 40 (1982), 169-178.
• [16] H. Lebesgue, Sur l'approximation des fonctions, Bull. Sci. Math. 22 (1898), 278-287.
• [17] J. Lukeš, J. Malý and L. Zajíček, Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math. 1189, Springer, 1985.
• [18] W. Rudin, Lebesgue's first theorem, in: Mathematical Analysis and Applications, Part B, Adv. Math. Suppl. Stud. 7b, Academic Press, 1981, 741-747.
• [19] S. Saks, Theory of the Integral, Dover, 1964.
• [20] W. Sierpiński, Sur les rapports entre l'existence des intégrales $∫_0^1 f(x,y)dx$, $∫_0^1 f(x,y)dy$, et $∫^1_0 dx∫_0^1 f(x,y)dy$, Fund. Math. 1 (1920), 142-147.
• [21] R. M. Solovay, A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math. 92 (1970), 1-56.
• [22] F. Tall, The density topology, Pacific J. Math. 62 (1976), 275-284.
• [23] Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1-54.