On measurability, pointwise convergence and compactness
Alexandra Ionescu Tulcea · Bulletin of the American Mathematical Society · 1974
The starting point of this investigation is the beautiful generalization of Egorov's theorem given by P. A. Meyer in Séminaire de Probabilités.V, (Strasbourg).The material is divided as follows:§1. Setting and terminology.§2.The Generalized Egorov Theorem.§3.An application to vector-valued mappings.§4.The ((separation property)) and the notion of lifting.Proofs of most of the results contained in this paper can be found in [5], [6], [7], [8].1. Setting and terminology.Throughout this article (E, ê, ju) will be a fixed probability space.We denote by «Sf=JS?(£', ê, ju) the algebra of all ƒ : E->R which are