×

zbMATH — the first resource for mathematics

Uniform boundedness theorems for k-triangular set functions. (English) Zbl 0726.28008
The author proves a version of Dieudonn√©’s boundedness theorem for k- triangular set functions with values in a commutative semigroup endowed with an invariant pseudometric. In the context of this paper it would be enough to examine \([0,+\infty[\)-valued set functions; such a function \(\phi\) is said to be k-triangular if \(\phi(\emptyset)=0\) and \(|\phi(A)- \phi(B)| \leq k\cdot \phi(B\setminus A)\) if \(A\subset B\).
Reviewer: H.Weber (Potenza)

MSC:
28B10 Group- or semigroup-valued set functions, measures and integrals
PDF BibTeX XML Cite