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Volumn 101, Issue 2, 2004, Pages 289-292

Hopf’s ratio ergodic theorem by inducing

Author keywords

Induced transformation; Pointwise ratio ergodic theorem

Indexed keywords


EID: 84979081950     PISSN: 00101354     EISSN: 17306302     Source Type: Journal    
DOI: 10.4064/cm101-2-11     Document Type: Article
Times cited : (18)

References (12)
  • 1
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    • Aaronson, J.1
  • 4
    • 0001625079 scopus 로고
    • Induced measure preserving transformations
    • S. Kakutani, Induced measure preserving transformations, Proc. Imp. Acad. Tokyo 19 (1943), 635–641.
    • (1943) Proc. Imp. Acad. Tokyo , vol.19 , pp. 635-641
    • Kakutani, S.1
  • 5
    • 0040955074 scopus 로고    scopus 로고
    • A simple proof of the ratio ergodic theorem
    • T. Kamae and M. Keane, A simple proof of the ratio ergodic theorem, Osaka J. Math. 34 (1997), 653–657.
    • (1997) Osaka J. Math , vol.34 , pp. 653-657
    • Kamae, T.1    Keane, M.2
  • 6
    • 51249186942 scopus 로고
    • A simple proof of some ergodic theorems
    • Y. Katznelson and B. Weiss, A simple proof of some ergodic theorems, Israel J. Math. 42 (1982), 291–296.
    • (1982) Israel J. Math. , vol.42 , pp. 291-296
    • Katznelson, Y.1    Weiss, B.2
  • 7
    • 85021071396 scopus 로고
    • The essence of the law of large numbers
    • Y. Takahashi (ed.), Plenum
    • M. Keane, The essence of the law of large numbers, in: Algorithms, Fractals, and Dynamics, Y. Takahashi (ed.), Plenum, 1995, 125–129.
    • (1995) Algorithms, Fractals, and Dynamics , pp. 125-129
    • Keane, M.1
  • 8
    • 0002286325 scopus 로고
    • Proof of the quasi-ergodic hypothesis
    • J. von Neumann, Proof of the quasi-ergodic hypothesis, Proc. Nat. Acad. Sci. U.S.A. 18 (1932), 70–82.
    • (1932) Proc. Nat. Acad. Sci. U.S.A. , vol.18 , pp. 70-82
    • Von Neumann, J.1
  • 10
    • 0003205961 scopus 로고    scopus 로고
    • The Ergodic Theory of Discrete Sample Paths
    • P. Shields, The Ergodic Theory of Discrete Sample Paths, Amer. Math. Soc., 1996.
    • (1996) Amer. Math. Soc
    • Shields, P.1
  • 11
    • 17244369457 scopus 로고
    • Sur une extension du théorème ergodique
    • W. Stepanoff [V. Stepanov], Sur une extension du théorème ergodique, Compos. Math. 3 (1936), 239–253.
    • (1936) Compos. Math , vol.3 , pp. 239-253
    • Stepanoff, W.1    Stepanov, V.2
  • 12
    • 0036258613 scopus 로고    scopus 로고
    • George David Birkhoff and John von Neumann: A question of priority and the ergodic theorems, 1931–1932
    • J. D. Zund, George David Birkhoff and John von Neumann: A question of priority and the ergodic theorems, 1931–1932, Historia Math. 29 (2002), 138–156.
    • (2002) Historia Math , vol.29 , pp. 138-156
    • Zund, J.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.