NEW SEQUENTIAL-COMPACTNESS RESULTS FOR SPACES OF SCALARLY INTEGRABLE FUNCTIONS

A new general relative sequential compactness criterion for scalarly integrable functions is presented. The novel feature of this result is the fact that it deals with a strong form of pointwise Cesaro-convergence (almost everywhere), which is stronger than the usual types of weak convergence. Applications of the main result include extensions of a classical weak compactness criterion for abstract L1-spaces and a recent relative sequential compactness criterion of Prohorov type for transition probabilites. The main result can also be seen as an abstract version of a famous theorem of Komlós, which is also essential for its proof. © 1990.