### 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.

#### Full Text:

PDFDOI: https://doi.org/10.2478/tatra.v52i0.182