Bisbas, A.; Karanikas, C. On the continuity of measures. (English) Zbl 0792.42014 Appl. Anal. 48, No. 1-4, 23-35 (1993). 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. Cited in 3 Documents MSC: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 43A05 Measures on groups and semigroups, etc. Keywords:Rademacher system; left Haar measure; Walsh functions × Cite Format Result Cite Review PDF Full Text: DOI References: [1] DOI: 10.1112/plms/s3-30.2.209 · Zbl 0325.43003 · doi:10.1112/plms/s3-30.2.209 [2] DOI: 10.1007/BF01571273 · Zbl 0726.42016 · doi:10.1007/BF01571273 [3] Graham C., Studia Math. LXV1 110 pp 213– (1980) [4] Graham C., Harmonic Analysis (1979) [5] DOI: 10.1016/S0076-5392(09)60415-X · doi:10.1016/S0076-5392(09)60415-X [6] Karanikas C., Boll. U. Mat. Ital 7 pp 331– (1990) [7] Zygmund A., Two vol This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.