| 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:
|
http://hdl.handle.net/10338.dmlcz/126207 |
| . |
| 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 |
| . |
