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

David C. Harris, William R. Wade
1978 Transactions of the American Mathematical Society  
We show that there exist uncountable sets of divergence for C(2U). We also show that a necessary and sufficient condition that a set E be a set of divergence for 1/(2"), 1 < p < oo, is that £ be of Haar measure zero.
doi:10.1090/s0002-9947-1978-0487242-7 fatcat:fb6gn4hgsbfhvmx6x7pmdk5p5y