Answer to Question #63678 in Real Analysis for Bright

Question

4.5. Let (X,E) and (Y,K) be two measurable spaces.
We equip the product space X × Y with the σ-algebra σ(Xˆ).

Will a subset of X × Y of the form

A×Y, A∈E

be measurable?

Will a subset of the form

X×B, B∈K be measurable? Is Yˆ a measurable map?