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Uniform boundedness theorems for k-triangular set functions. (English) Zbl 0726.28008
The author proves a version of Dieudonné’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