Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

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


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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42A56

Retrieve articles in all journals with MSC: 42A56


Additional Information

Keywords: Walsh functions, Rademacher functions, homogeneous Banach spaces, the group <!– MATH ${2^\omega }$ –> <IMG WIDTH="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img4.gif" ALT="${2^\omega }$">, sets of divergence
Article copyright: © Copyright 1978 American Mathematical Society