On sets nonmeasurable with respect to invariant measures

Slawomir Solecki

Research output: Contribution to journalArticlepeer-review


A group G acts on a set X, and μ is a G-invariant measure on X. Under certain assumptions on the action of G and on μ (e.g., G acts freely and is uncountable, and μ is σ-finite), we prove that each set of positive μ-measure contains a subset nonmeasurable with respect to any invariant extensions of μ. We study the case of ergodic measures in greater detail.

Original languageEnglish (US)
Pages (from-to)115-124
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Sep 1993


  • Extensions of measures
  • Invariant measures
  • Nonmeasurable sets

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


Dive into the research topics of 'On sets nonmeasurable with respect to invariant measures'. Together they form a unique fingerprint.

Cite this