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The pathological infinity of measures. (English) Zbl 0596.28001
Summary: We propose and study the notion of pathological infinity of measures. If (X,S,$$\mu)$$ is a measure space then $$A\in S$$ is called a pathological infinity if $$\mu (A)=\infty$$, A does not contain a set of positive finite measure and A contains no infinite atom.
In Section 1 we introduce theorems connected with the role of the pathological infinity in classification of properties of infinite measures. These are: the characterization of semifiniteness (Theorem 1) and the characterization of countable chain condition of nonnegative measures without pathological infinity. In Section 2 a measurable space admitting the pathological infinity is studied.

##### MSC:
 28A12 Contents, measures, outer measures, capacities 28A60 Measures on Boolean rings, measure algebras