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Sectionwise properties and measurability of functions of two variables. (English) Zbl 0519.26007
MSC:
26B35 Special properties of functions of several variables, Hölder conditions, etc.
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
26A21 Classification of real functions; Baire classification of sets and functions
Citations:
Zbl 0382.26005
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References:
[1] A. M. Bruckner,Differentiation of Real Functions, Lecture Notes in Math. No. 659, Springer (Berlin, Heidelberg, New York, 1978). · Zbl 0382.26002
[2] R. O. Davies, Separate approximate continuity implies measurability,Proc. Camb. Phil. Soc.,73 (1973), 461–465. · Zbl 0254.26011
[3] R. O. Davies and J. Dravecký, On the measurability of functions of two variables,Mat. Časopis,23 (1973), 285–289. · Zbl 0262.28004
[4] Z. Grande, La mesurabilité des fonctions de deux variables,Bull. Acad. Polon. Sci. Math. Astr. Phys.,22 (1974), 657–661. · Zbl 0287.28003
[5] Z. Grande, Quelques remarques sur les classes de Baire des fonctions de deux variables,Mat. Časopis,26 (1976), 241–246. · Zbl 0382.26005
[6] Z. Grande, Sur les fonctions de deux variables dont les coupes sont des dérivées,Proc. Amer. Math. Soc.,57 (1976), 69–74. · Zbl 0305.26005
[7] C. Kuratowski,Topologie I (Warszawa, 1958).
[8] M. Laczkovich, On the measurability of functions whose sections are derivatives.,Periodica Math. Hung.,12 (1981), 243–254. · Zbl 0449.26009
[9] M. Laczkovich, On the Baire class of functions of two variables, to appear inFund. Math. · Zbl 0378.26006
[10] J. S. Lipiński, On measurability of functions of two variables,Bull. Acad. Polon. Sci. Math. Astr. Phys.,20 (1972), 131–135. · Zbl 0228.28009
[11] W. Sierpiński, Sur les rapports entre l’existence des intégrales \(\mathop \smallint \limits_0^1 f(x,y)dx, \mathop \smallint \limits_0^1 f(x,y)dy\) et \(\mathop \smallint \limits_0^1 dx \mathop \smallint \limits_0^1 f(x,y)dy\) ,Fund. Math.,1 (1920), 142–147.
[12] Z. Zahorski, Sur la première dérivée,Trans. Amer. Math. Soc.,69 (1950), 1–54.
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