A note on measurability of multifunctions approximately continuous in second variable
Abstract
Let $I\subset \R$ be an interval, $(X,{\cal
M}(X))$ a measure space, and $(Z,||\cdot||)$ a reflexive Banach
space. We prove that a multifunction $F$ from $X\times I$ to $Z$ is
measurable whenever it is ${\cal M}(X)$-measurable in the first and
approximately continuous and almost everywhere continuous in the
second variable.
M}(X))$ a measure space, and $(Z,||\cdot||)$ a reflexive Banach
space. We prove that a multifunction $F$ from $X\times I$ to $Z$ is
measurable whenever it is ${\cal M}(X)$-measurable in the first and
approximately continuous and almost everywhere continuous in the
second variable.
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PDFDOI: https://doi.org/10.2478/tatra.v52i0.182