Preliminaries

In this part we state definitions (and notations) and conventions having been used throughout this work.i) DEFINITIONS and NOTATIONSWe start with recalling known definitions and characterizations within linear topological vector spaces, (stochastic) (convex) analysis, measure and probability theory. For that which is outlined below, we mainly used Feller 1966 [44], Billingsley 1968 [9], Rockafellar 1970 [118] and 1976 [121], Halmos 1974 [55], Kelley and Namioka 1976 [80], Ekeland and Temam 1976 [39], Castaing and Valadier 1976 [20], Brøndsted 1983 [18], Prékopa 1980 [107], Rudin 1980 [131], Robinson 1987 [111], Wets 1989 [144] and Bauer 1990 [3].