On some conditions which imply the continuity of almost all sections
Mathematica Bohemica (1994)
- Volume: 119, Issue: 1, page 49-56
- ISSN: 0862-7959
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topGrande, Zbigniew. "On some conditions which imply the continuity of almost all sections $x \rightarrow f(t,x)$." Mathematica Bohemica 119.1 (1994): 49-56. <http://eudml.org/doc/29361>.
@article{Grande1994,
abstract = {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.},
author = {Grande, Zbigniew},
journal = {Mathematica Bohemica},
keywords = {Lebesgue measure; density; Baire property; category; continuity; quasi- continuity; sections; measure; Lebesgue measure; density; Baire property; category; continuity; quasi- continuity; sections},
language = {eng},
number = {1},
pages = {49-56},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some conditions which imply the continuity of almost all sections $x \rightarrow f(t,x)$},
url = {http://eudml.org/doc/29361},
volume = {119},
year = {1994},
}
TY - JOUR
AU - Grande, Zbigniew
TI - On some conditions which imply the continuity of almost all sections $x \rightarrow f(t,x)$
JO - Mathematica Bohemica
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 119
IS - 1
SP - 49
EP - 56
AB - 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.
LA - eng
KW - Lebesgue measure; density; Baire property; category; continuity; quasi- continuity; sections; measure; Lebesgue measure; density; Baire property; category; continuity; quasi- continuity; sections
UR - http://eudml.org/doc/29361
ER -
References
top- Bruckner A.M., Differentiation of real functions, Lecture Notes in Math. 659 (1978). Springer, Berlin, Heidelberg, New York. (1978) Zbl0382.26002MR0507448
- Grande Z., On the Carathéodory's superposition, sent to Real Anal. Exch. MR1268853
- Grande Z., 10.4064/fm-93-3-155-160, Fund. Math. 93 (1976), 155-160. (1976) MR0432847DOI10.4064/fm-93-3-155-160
- Grande Z., 10.4064/fm-115-2-119-125, Fund. Math. 115 (1983), 119-125. (1983) Zbl0515.26008MR0699877DOI10.4064/fm-115-2-119-125
- O'Malley R.J., 10.2140/pjm.1977.72.207, Pacific J. Math. 72 (1977), 207-222. (1977) Zbl0339.26011MR0447499DOI10.2140/pjm.1977.72.207
- Neubrunn T., 10.2307/44151947, Real Anal. Exch. 14 (1988-89), no. 2, 259-306. (1988) MR0995972DOI10.2307/44151947
- Sierpiński W., 10.4064/fm-1-1-112-115, Fund. math. 1 (1920), 112-115. (1920) DOI10.4064/fm-1-1-112-115
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