ON A PROJECTION THEOREM FOR MULTIFUNCTIONS

Abstract

Let (T,μ) be a complete measurable space, u a Suslin space and B(u) the Borel σ-algebra of u. The projection theorem, see for example [3], p. 75, states that if the set A belongs to the σ-algebra generated by the class μ x B(U), then its projection P_T(A) belongs to the σ-algebra μ. The aim of this note is to show that the projection theorem fails if (T,μ) is incomplete.