Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions

Giovanni Anello; Paolo Cubiotti

Annales Polonici Mathematici (2004)

  • Volume: 83, Issue: 2, page 179-187
  • ISSN: 0066-2216

Abstract

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We consider a multifunction F : T × X → 2 E , where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.

How to cite

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Giovanni Anello, and Paolo Cubiotti. "Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions." Annales Polonici Mathematici 83.2 (2004): 179-187. <http://eudml.org/doc/280456>.

@article{GiovanniAnello2004,
abstract = {We consider a multifunction $F:T×X → 2^E$, where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.},
author = {Giovanni Anello, Paolo Cubiotti},
journal = {Annales Polonici Mathematici},
keywords = {lower semicontinuity},
language = {eng},
number = {2},
pages = {179-187},
title = {Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions},
url = {http://eudml.org/doc/280456},
volume = {83},
year = {2004},
}

TY - JOUR
AU - Giovanni Anello
AU - Paolo Cubiotti
TI - Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions
JO - Annales Polonici Mathematici
PY - 2004
VL - 83
IS - 2
SP - 179
EP - 187
AB - We consider a multifunction $F:T×X → 2^E$, where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.
LA - eng
KW - lower semicontinuity
UR - http://eudml.org/doc/280456
ER -

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