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.


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