Two counterexamples, addressing questions raised in Adamczak (2019) and Poly Zheng (2019), are provided. Both counterexamples related to chaoses. Let F n = Y + Z , where the random variables belong different chaoses of uniformly bounded degree. It may be that ? a . s 0 L 2 ? E { sup | } < ? for some > yet fails converge a.s.

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure &theta; : R &rarr; L(P, Q), where R is a &sigma;-ring of subsets of X&ne; &empty;, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...