The atoms of a countable sum of set functions. (English) Zbl 0665.28003

The set of atoms of a nonnegative set function which is a countable sum of nonnegative set functions is expressed. An analogous theorem for semigroup valued measures is given. Moreover it is shown that the sum of countably many atomic measures is an atomic measure.


28A10 Real- or complex-valued set functions
28A12 Contents, measures, outer measures, capacities
28B10 Group- or semigroup-valued set functions, measures and integrals
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