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

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1. [1] T. Bartoszyński and S. Shelah, Closed measure zero sets, Ann. Pure Appl. Logic 58 (1992), 93-110. Zbl0764.03018
2. [2] J. Bourgain, D. H. Fremlin and M. Talagrand, Pointwise compact sets of Baire measurable functions, Amer. J. Math. 100 (1978), 845-886. Zbl0413.54016
3. [3] A. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. 659, Springer, 1978. Zbl0382.26002
4. [4] T. Carlson, Extending Lebesgue measure by infinitely many sets, Pacific J. Math. 115 (1984), 33-45. Zbl0582.28004
5. [5] R. O. Davies, Separate approximate continuity implies measurability, Proc. Cambridge Philos. Soc. 73 (1973), 461-465. Zbl0254.26011
6. [6] R. O. Davies and J. Dravecký, On the measurability of functions of two variables, Mat. Časopis 23 (1973), 285-289. Zbl0262.28004
7. [7] A. Denjoy, Sur les fonctions dérivées sommables, Bull. Soc. Math. France 43 (1916), 161-248. Zbl45.0435.03
8. [8] C. Freiling, Axioms of symmetry: throwing darts at the real number line, J. Symbolic Logic 51 (1986), 190-200. Zbl0619.03035
9. [9] C. Goffman, C. J. Neugebauer and T. Nishiura, Density topology and approximate continuity, Duke Math. J. 28 (1961), 497-506. Zbl0101.15502
10. [10] Z. Grande, La mesurabilité des fonctions de deux variables, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 22 (1974), 657-661. Zbl0287.28003
11. [11] T. Jech, Set Theory, Academic Press, 1978. 
12. [12] P. Komjáth, Some remarks on second category sets, Colloq. Math. 66 (1993), 57-62. Zbl0827.03031
13. [13] K. Kunen, Random and Cohen reals, in: Handbook of Set-Theoretic Topology, North-Holland, 1984, 887-911. 
14. [14] K. Kuratowski, Topology, Vol. 1, Academic Press, 1966. 
15. [15] M. Laczkovich and G. Petruska, Sectionwise properties and measurability of functions of two variables, Acta Math. Acad. Sci. Hungar. 40 (1982), 169-178. Zbl0519.26007
16. [16] H. Lebesgue, Sur l'approximation des fonctions, Bull. Sci. Math. 22 (1898), 278-287. 
17. [17] J. Lukeš, J. Malý and L. Zajíček, Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math. 1189, Springer, 1985. Zbl0607.31001
18. [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. [19] S. Saks, Theory of the Integral, Dover, 1964. 
20. [20] W. Sierpiński, Sur les rapports entre l’existence des intégrales ${\int }_0^{1}f(x,y)dx$, ${\int }_0^{1}f(x,y)dy$, et ${\int }_0^{1}dx{\int }_0^{1}f(x,y)dy$, Fund. Math. 1 (1920), 142-147. Zbl47.0245.01
21. [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. Zbl0207.00905
22. [22] F. Tall, The density topology, Pacific J. Math. 62 (1976), 275-284. Zbl0305.54039
23. [23] Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1-54. Zbl0038.20602