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Keywords:
Lebesgue measure; density; Baire property; category; continuity; quasi- continuity; sections; measure
Lebesgue measure; density; Baire property; category; continuity; quasi- continuity; sections; measure
Summary:
Let $I$ be an open interval, $X$ a topological space and $Y$ a metric space. Some local conditions implying continuity and quasicontinuity of almost all sections $x\rightarrow f(t,x)$ of a function $f: I\times X\rightarrow Y$ are shown.
References:
[1] Bruckner A.M.: Differentiation of real functions. Lecture Notes in Math. 659 (1978). Springer, Berlin, Heidelberg, New York. MR 0507448 | Zbl 0382.26002
[2] Grande Z.: On the Carathéodory's superposition. sent to Real Anal. Exch. MR 1268853
[3] Grande Z.: Les fonctions qui ont la pгopriété (K) et la mesurabilité de fonctions de deux variables. Fund. Math. 93 (1976), 155-160. DOI 10.4064/fm-93-3-155-160 | MR 0432847
[4] Grande Z.: Sur les classes de Baire des fonctions de deux variables. Fund. Math. 115 (1983), 119-125. DOI 10.4064/fm-115-2-119-125 | MR 0699877 | Zbl 0515.26008
[5] O'Malley R.J.: Approximately differentiable functions. The r-topology. Pacific J. Math. 72 (1977), 207-222. DOI 10.2140/pjm.1977.72.207 | MR 0447499 | Zbl 0339.26011
[6] Neubrunn T.: Quasi-continuity. Real Anal. Exch. 14 (1988-89), no. 2, 259-306. DOI 10.2307/44151947 | MR 0995972
[7] Sierpiński W.: Sur un problème concernant les ensembles mesurables superficiellement. Fund. math. 1 (1920), 112-115. DOI 10.4064/fm-1-1-112-115
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