Convolutions and absolute continuity
Author:
D. A. Lind
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
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Abstract | Similar Articles | Additional Information
Abstract: We show that if 
is a subset of the circle with positive Lebesgue measure, and 
is integrable on almost every translate of 
, then 
is integrable on the whole circle. A generalization of this fact leads to a characterization of positive measures with nonvanishing absolutely continuous part.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1973-0320257-9
Keywords:
Compact group,
integrable on translates,
positive measure,
singular measure,
finiteness of convolutions,
absolute continuity
Article copyright:
© Copyright 1973
American Mathematical Society
