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

Tom 83 / 2004

Giovanni Anello, Paolo Cubiotti Annales Polonici Mathematici 83 (2004), 179-187 MSC: 47H04, 28B20, 34A60. DOI: 10.4064/ap83-2-8

Streszczenie

We consider a multifunction $F:T\times X\to 2^E$, 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.

Autorzy

  • Giovanni AnelloDepartment of Mathematics
    University of Messina
    Contrada Papardo, Salita Sperone 31
    98166 Messina, Italy
    e-mail
  • Paolo CubiottiDepartment of Mathematics
    University of Messina
    Contrada Papardo, Salita Sperone 31
    98166 Messina, Italy
    e-mail

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