On some conditions which imply the continuity of almost all sections x f ( t , x )

Zbigniew Grande

Mathematica Bohemica (1994)

  • Volume: 119, Issue: 1, page 49-56
  • ISSN: 0862-7959

Abstract

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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 f ( t , x ) of a function f : I × X Y are shown.

How to cite

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Grande, 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

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  1. Bruckner A.M., Differentiation of real functions, Lecture Notes in Math. 659 (1978). Springer, Berlin, Heidelberg, New York. (1978) Zbl0382.26002MR0507448
  2. Grande Z., On the Carathéodory's superposition, sent to Real Anal. Exch. MR1268853
  3. Grande Z., 10.4064/fm-93-3-155-160, Fund. Math. 93 (1976), 155-160. (1976) MR0432847DOI10.4064/fm-93-3-155-160
  4. Grande Z., 10.4064/fm-115-2-119-125, Fund. Math. 115 (1983), 119-125. (1983) Zbl0515.26008MR0699877DOI10.4064/fm-115-2-119-125
  5. 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
  6. Neubrunn T., 10.2307/44151947, Real Anal. Exch. 14 (1988-89), no. 2, 259-306. (1988) MR0995972DOI10.2307/44151947
  7. 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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