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On the continuity of measures. (English) Zbl 0792.42014

Summary: We construct continuous singular (with respect to the left Haar measure) Riesz-type measures, whose convolution action on a norm compact subset of continuous measures is in \(L_ 1\). A byproduct of the proof is a Wiener- type characterization of continuous measures on measurable spaces in terms of Walsh functions.

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
43A05 Measures on groups and semigroups, etc.
Full Text: DOI

References:

[1] DOI: 10.1112/plms/s3-30.2.209 · Zbl 0325.43003 · doi:10.1112/plms/s3-30.2.209
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