Second order ergodic theorems for ergodic transformations of infinite measure spaces
Authors:
Jon Aaronson, Manfred Denker and Albert M. Fisher
Journal:
Proc. Amer. Math. Soc. 114 (1992), 115127
MSC:
Primary 28D05; Secondary 60F15
MathSciNet review:
1099339
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Abstract: For certain pointwise dual ergodic transformations we prove almost sure convergence of the logaverages and the ChungErdös averages towards , where denotes the return sequence of .
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 [1]
 J. Aaronson, Ergodic theory for inner functions of the upper half plane, Ann. Inst. H. Poincaré. Anal. Non Linéaire 14 (1978), 233253. MR 508928 (80b:28018)
 [2]
 , The asymptotic distributional behaviour of transformations preserving infinite measures, J. D'Analyse Math. 39 (1981), 203234. MR 632462 (82m:28030)
 [3]
 , Random expansions, Ann. Prob. 14 (1986), 10371057. MR 841603 (87k:60057)
 [4]
 T. Bedford and A. M. Fisher, Analogues of the Lebesgue density theorem for fractal subsets of the reals and integers, Proc. London Math. Soc. (to appear).
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 K. L. Chung and P. Erdös, Probability limit theorems assuming only the first moment. I, Mem. Amer. Math. Soc. 6 (1951). MR 0040612 (12:722g)
 [6]
 W. Feller, An Introduction to probability theory and its applications 2, Wiley, New York, 1971. MR 0270403 (42:5292)
 [7]
 A. M. Fisher, A pathwise central limit theorem for random walks, Ann. Prob. (to appear).
 [8]
 , Integer Cantor sets and an ordertwo ergodic theorem, J. D'Analyse Math. (to appear).
 [9]
 G. Letac, Which functions preserve Cauchy laws, Proc. Amer. Math. Soc. 67 (1977), 277286. MR 0584393 (58:28433)
 [10]
 M. Thaler, Transformations on with infinite invariant measures, Israel J. Math. 46 (1983), 6796. MR 727023 (85g:28020)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199210993394
PII:
S 00029939(1992)10993394
Article copyright:
© Copyright 1992
American Mathematical Society
