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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 rst 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. 1. Introduction. If X is a topological space, we denote byB(X) the Borel -algebra ofX. Moreover, if is measure onB(X), we denote byT (X) the completion ofB(X) with respect to . We briey putT =T (X) when ambiguities do not occur. For the basic denitions about multifunctions, we refer the reader to (6) and (7). This note is motivated by the main result of (11), which concerns the existence of Riemann-measurable selections (i.e., selections which are a.e. continuous) for a given multifunction. For the reader's convenience, we now state the main result of (11) (as usual, by a Polish space we mean a complete separable metric space).

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