Previous |  Up |  Next


Title: On some conditions which imply the continuity of almost all sections $x \to f(t,x)$ (English)
Author: Grande, Zbigniew
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 119
Issue: 1
Year: 1994
Pages: 49-56
Summary lang: English
Category: math
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. (English)
Keyword: Lebesgue measure
Keyword: density
Keyword: Baire property
Keyword: category
Keyword: continuity
Keyword: quasi- continuity
Keyword: sections
Keyword: measure
MSC: 26B05
MSC: 26B99
MSC: 28A10
MSC: 54C08
idZBL: Zbl 0817.26002
idMR: MR1303551
DOI: 10.21136/MB.1994.126207
Date available: 2009-09-24T21:02:45Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] Bruckner A.M.: Differentiation of real functions.Lecture Notes in Math. 659 (1978). Springer, Berlin, Heidelberg, New York. Zbl 0382.26002, MR 0507448
Reference: [2] Grande Z.: On the Carathéodory's superposition.sent to Real Anal. Exch. MR 1268853
Reference: [3] Grande Z.: Les fonctions qui ont la pгopriété (K) et la mesurabilité de fonctions de deux variables.Fund. Math. 93 (1976), 155-160. MR 0432847, 10.4064/fm-93-3-155-160
Reference: [4] Grande Z.: Sur les classes de Baire des fonctions de deux variables.Fund. Math. 115 (1983), 119-125. Zbl 0515.26008, MR 0699877, 10.4064/fm-115-2-119-125
Reference: [5] O'Malley R.J.: Approximately differentiable functions. The r-topology.Pacific J. Math. 72 (1977), 207-222. Zbl 0339.26011, MR 0447499, 10.2140/pjm.1977.72.207
Reference: [6] Neubrunn T.: Quasi-continuity.Real Anal. Exch. 14 (1988-89), no. 2, 259-306. MR 0995972, 10.2307/44151947
Reference: [7] Sierpiński W.: Sur un problème concernant les ensembles mesurables superficiellement.Fund. math. 1 (1920), 112-115. 10.4064/fm-1-1-112-115


Files Size Format View
MathBohem_119-1994-1_5.pdf 1.099Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo