×

zbMATH — the first resource for mathematics

On category of mixing in infinite measure spaces. (English) Zbl 0226.28008

MSC:
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
60B11 Probability theory on linear topological spaces
28D99 Measure-theoretic ergodic theory
PDF BibTeX Cite
Full Text: DOI
References:
[1] D. Blackwell andD. Freedman, The tail{\(\sigma\)}-field of a Markov chain and a theorem of Orey,Ann. Math. Statist. 35 (1964), 1291–1295. · Zbl 0127.35204
[2] P. R. Halmos, In general a measure-preserving transformation is mixing,Ann. of Math. (2)45 (1944), 786–792. · Zbl 0063.01889
[3] P. R. Halmos,Measure Theory, Van Nostrand, New York, 1950.
[4] P. R. Halmos,Lectures on Ergodic Theory, Mathematical Society of Japan, Tokyo, 1956.
[5] S. Kakutani andW. Parry, Infinite measure-preserving transformations with ”mixing”,Bull. Amer. Math. Soc. 69 (1963), 752–756. · Zbl 0126.31801
[6] E. M. Klimko andL. Sucheston, On convergence of information in spaces with infinite invariant measure,Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 10 (1968), 226–235. · Zbl 0165.53401
[7] B. O. Koopman andJ. von Neumann, Dynamical systems of continuous spectra,Proc. Nat. Acad. Sci. U.S.A. 18 (1932), 255–263. · Zbl 0006.22702
[8] U. Krengel, Entropy of conservative transformations,Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1966), 161–181. · Zbl 0183.19303
[9] U. Krengel andL. Sucheston, On mixing in infinite measure spaces,Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 150–164. · Zbl 0176.33804
[10] K. Krickeberg, Mischende Transformationen auf Mannigfaltigkeiten unendlichen Masses,Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 (1967), 235–247. · Zbl 0158.16503
[11] V. A. Rokhlin, A ”general” measure-preserving transformation is not mixing,Dokl. Akad. Nauk SSSR (NS)60 (1948), 349–351. (Russian) · Zbl 0033.06601
[12] L. Sucheston, A note on conservative transformations and the recurrence theorem,Amer. J. Math. 79 (1957), 444–447. · Zbl 0077.27002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.