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Variations on a theme of Debs and Saint Raymond
Author(s) -
Körner T. W.
Publication year - 2009
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn059
Subject(s) - saint , theme (computing) , geography , history , art history , computer science , world wide web
A famous theorem of Debs and Saint Raymond states that the complement of a set of first category is of strong multiplicity. We prove a theorem which combines this with a result of Rudin which states that independent closed sets of strong multiplicity exist. We also prove a theorem which combines the theorem of Debs and Saint Raymond with a theorem of Wiener and Wintner which states that there exists a measure with singular support whose convolution square is absolutely continuous.