A strong form of spectral resolution
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We consider pseudo-measures T on totally disconnected sets E as finitely additive set functions whit the usual variation norm ‖ ‖v. If\(E \subseteq R/2\prod Z\), m(E)=0, T=f′, f ∈L1, and ‖T‖v<∞ then T is a measure. For arbitrary locally compact abelian groups we give conditions that T be a measure in terms of the pseudo-measure norm; this result is known for R/2ΠZ.
KeywordsAbelian Group Variation Norm Strong Form Compact Abelian Group Spectral Resolution
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