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A Note on the Kawada-into Theorem

Published online by Cambridge University Press:  20 January 2009

John S. Pym
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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

References

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