Annali di Matematica Pura ed Applicata

, Volume 86, Issue 1, pp 313–324 | Cite as

A strong form of spectral resolution

  • John J. Benedetto


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/Z.


Abelian Group Variation Norm Strong Form Compact Abelian Group Spectral Resolution 
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Copyright information

© Nicola Zanichelli Editore 1970

Authors and Affiliations

  • John J. Benedetto
    • 1
  1. 1.U.S.A.

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