Über mittlere Rückkehrzeit unter einer maßtreuen Strömung

G. Helmberg

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)


Let T be a one-parameter semigroup of measure preserving transformations of a probability space. The theorem of Kac on mean recurrence time of the points x in a measurable subset E under a discrete semigroup is carried over to the case of a flow T with continuous time parameter t0. Recurrence time is defined as the infimum of these parameter values t>0 for which the orbit of x has returned to E after having temporarily left the set E. The results are first formulated for a probability space without any topological structure; they are then applied to the case of a continuous flow in a compact metric space.
Original languageEnglish
Pages (from-to)165-179
Number of pages15
JournalZeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete
Issue number2
Publication statusPublished - 1969


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