Geodesic
Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions
Giovanni Anello1 ; Paolo Cubiotti1
1Department of Mathematics University of Messina Contrada Papardo, Salita Sperone 31 98166 Messina, Italy
Annales Polonici Mathematici, Tome 83 (2004) no. 2, pp. 179-187
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap83-2-8
Keywords: consider multifunction times where separable metric spaces complete assuming jointly measurable product lower semicontinuous second variable establish existence selection which measurable respect first variable continuous respect second result spirit where multifunctions only variable considered

Giovanni Anello  1   ; Paolo Cubiotti  1

1 Department of Mathematics University of Messina Contrada Papardo, Salita Sperone 31 98166 Messina, Italy 
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     title = {Parametrization of {Riemann-measurable
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     journal = {Annales Polonici Mathematici},
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 with application to differential inclusions
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Giovanni Anello; Paolo Cubiotti. Parametrization of Riemann-measurable
 selections for multifunctions of two variables
 with application to differential inclusions. Annales Polonici Mathematici, Tome 83 (2004) no. 2, pp. 179-187. doi: 10.4064/ap83-2-8

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