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On the relations between continuous and nonatomic measures

โœ Scribed by Wolfgang Adamski

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
338 KB
Volume
99
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

On the relations between continuous and nonatomic measures

By WOLFGANG ADAMSKI of Munchen (Eingegangen am 21. 5. 1979)

It is the purpose of this paper to study the relations between continuous and nonatomic (finite, nonnegative, countably additive) measures, where a measure defined on a o-algebra %of subsets of a set X is said to be continuous if every %-atom has outer measure zero. It will be shown that every nonatomic measure is continuous and that tho converse is true iff X is %-complete (in the sense of [l]). If the %-atoms are countahlv determined, (in particular, if % is countably generated or countably separating,) then every continuous measure on is nonatomic. Finally, the general results are applied to soiiie topological situations.

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