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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Sets of divergence on the group $ 2\sp{\omega }$


Authors: David C. Harris and William R. Wade
Journal: Trans. Amer. Math. Soc. 240 (1978), 385-392
MSC: Primary 42A56
DOI: https://doi.org/10.1090/S0002-9947-1978-0487242-7
MathSciNet review: 0487242
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Abstract: We show that there exist uncountable sets of divergence for $ C({2^\omega })$. We also show that a necessary and sufficient condition that a set E be a set of divergence for $ {L^p}({2^\omega }),1 < p < \infty $, is that E be of Haar measure zero.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0487242-7
Keywords: Walsh functions, Rademacher functions, homogeneous Banach spaces, the group $ {2^\omega }$, sets of divergence
Article copyright: © Copyright 1978 American Mathematical Society