Convolutions and absolute continuity
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- by D. A. Lind PDF
- Proc. Amer. Math. Soc. 39 (1973), 347-348 Request permission
Abstract:
We show that if $E$ is a subset of the circle with positive Lebesgue measure, and $g$ is integrable on almost every translate of $E$, then $g$ is integrable on the whole circle. A generalization of this fact leads to a characterization of positive measures with nonvanishing absolutely continuous part.References
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 347-348
- MSC: Primary 28A10; Secondary 43A05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0320257-9
- MathSciNet review: 0320257