Finitely subadditive outer measures, finitely superadditive inner measures and their measurable sets
Consider any set X. A finitely subadditive outer measure on P(X) is defined to be a function v from P(X) to R such that v(ϕ)=0 and v is increasing and finitely subadditive. A finitely superadditive inner measure on P(X) is defined to be a function p from P(X) to R such that p(ϕ)=0 and p is increasin...
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Format: | Article |
Language: | English |
Published: |
Hindawi Limited
1996-01-01
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Series: | International Journal of Mathematics and Mathematical Sciences |
Subjects: | |
Online Access: | http://dx.doi.org/10.1155/S016117129600066X |
Summary: | Consider any set X. A finitely subadditive outer measure on P(X) is defined to be
a function v from P(X) to R such that v(ϕ)=0 and v is increasing and finitely subadditive. A finitely
superadditive inner measure on P(X) is defined to be a function p from P(X) to R such that p(ϕ)=0 and p is increasing and finitely superadditive (for disjoint unions) (It is to be noted that every finitely
superadditive inner measure on P(X) is countably superadditive). |
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ISSN: | 0161-1712 1687-0425 |