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Union results for thin sets

Published online by Cambridge University Press:  18 May 2009

Kathryn E. Hare
Kathryn E. Hare
Affiliation:
Department of Pure MathematicsUniversity of WaterlooWaterloo, Ontari O N2L 3G1 Canada
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Let G be a compact abelian group and let Γ be its (discrete) dual group. Denote by M(G) the space of complex regular Borel measures on G.

Let E be a subset of Γ. Then:

(i) E is called a Rajchman set if, for all μ ∈M(G) implies

(ii) E is called a set of continuity if given ε > 0 there exists δ > 0 such that if and

(iii) E is called a parallelepiped of dimension N if |E| = 2N and there are two-element sets . (The multiplication indicated here is the group operation.)

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 2 , May 1990 , pp. 241 - 254
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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