A note on measurability of multifunctions approximately continuous in second variable

Let I ⊂R be an interval,(X,ℳ(X)) a measure space, and (Z, ∥⋅∥) a reflexive Banach space. We prove that a multifunction F from X × I to Z is measurable whenever it is ℳ(X)-measurable in the first and approximately continuous and almost everywhere continuous in the second variable.