Potential theory of Monge-Ampère on a Banach space. Minimum principle and Poisson property (Q1917789)

Based on the study of the Monge-Ampère equation on a Banach space, E. M. J. Bertin built up the basis for a potential theory on a nonlocally compact space. Continuing this process in a separable Banach space that is reflexive, the author proves here the analogues of the minimum principle and the Poisson modifications for hyperharmonic functions; the weak compactness and the Baire property stand in for the local compactness in the classical proofs.