On projections of finitely additive measures

Thomas Jech, Karel Prikry

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A theorem of Z. Frolik and M. E. Rudin states that for every two-valued measure μ on N, if F: N → N is such that F* (μ) = μ then F(x) = x for almost all x. We prove that a generalization of this theorem fails for measures in general: Theorem. There exist a translation invariant measure μ on N and a function F: N → N such that F* (μ) = μ, and if A ⊆ N is such that F is one-to-one on A, then μ (A) ≤ 1/2.

Original languageEnglish (US)
Pages (from-to)161-165
Number of pages5
JournalProceedings of the American Mathematical Society
Volume74
Issue number1
DOIs
StatePublished - Apr 1979

Keywords

  • Finitely additive measure
  • Integral
  • Projection
  • Two-valued measure
  • Ultrafilter
  • Ultrafilter limit

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