On Topologies and Boundaries In Potential Theory. Lecture Notes in Mathematics 175

by M. Brelot

General notions of thinness and fine topology.- Notion of reduced function. Applications. Strong thinness and strong unthinness.- General results on fine limits.- Quasi-topological notions.- Weak thinness.- Notions in classical potential theory.- Classical fine topology-general properties.- Applications to balayage, weights and capacities.- Further study of classical thinness. Some applications.- Relations with the Choquet boundary.- Extension to axiomatic theories of harmonic functions.- Abstract minimal thinness, minimal boundary, minimal fine topology.- General compactification of constantinescu-cornea first examples of application.- Classical martin space the martin integral representation.- Classical martin space and minimal thinness.- Classical martin boundary dirichlet problem and boundary behaviour.- Comparison of both thinnesses. Fine limits and non-tangential limits. (Classical case. Examples).- Martin space and minimal thinness in axiomatic theories - short survey.

176 pages, Paperback

First published March 28, 1971