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A Note on the Kawada-into Theorem
Published online by Cambridge University Press: 20 January 2009
Extract
If µ is a bounded regular Borel measure on a locally compact group G, and L1(G) denotes the class of complex-valued functions which are integrable with respect to the left Haar measure m of G, then, for each f∈L1(G),
defines almost everywhere (a.e.) with respect to m a function μ*f which is again in L1(G). The measure μ will be called isotone on G mapping f→μ*f is isotone, i.e. f≧0 a.e. (m) if and only if μ*f≧0 a.e. (m).
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 4 , December 1963 , pp. 295 - 296
- Copyright
- Copyright © Edinburgh Mathematical Society 1963
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