Cardinal algebras of functions and integration
Choquet integrals in potential theory.
This is a survey of various applications of the notion of the Choquet integral to questions in Potential Theory, i.e. the integral of a function with respect to a non-additive set function on subsets of Euclidean n-space, capacity. The Choquet integral is, in a sense, a nonlinear extension of the standard Lebesgue integral with respect to the linear set function, measure. Applications include an integration principle for potentials, inequalities for maximal functions, stability for solutions to...
Compact sets of tight measures
Completeness of spaces over finitely additive probabilities
Continuity and the subdivision norm infimum function