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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

REFERENCES

Halmos, P. R.Measure Theory (van Nostrand, New York, 1950).CrossRefGoogle Scholar
Kawada, Y.On the group ring of a topological group, Math. Jap. 1 (1948), 1–5.Google Scholar
Loomis, L. H.Abstract Harmonic Analysis (van Nostrand, New York, 1953).Google Scholar
Macbeath, A. M. and Swierczkowski, S.Measures in homogeneous spaces, Fund. Math. 49 (1960), 15–24.CrossRefGoogle Scholar
Williamson, J. H.On theorems of Kawada and Wendel, Proc. Edinburgh Math. Soc. 11 (1958), 71–77.CrossRefGoogle Scholar