Conditions are developed from
which one may infer that a measurable subset S of an LCA group Ĝ is a Riesz set,
or in general, a small p set. Subsets of inverse images of small p sets under continuous
homomorphisms which are small q sets for some q are investigated. These
considerations yield extensions to LCA groups of Bochner’s version of the F. and M.
Riesz theorem.