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), 115-127

MSC:
Primary 28D05; Secondary 60F15

DOI:
https://doi.org/10.1090/S0002-9939-1992-1099339-4

MathSciNet review:
1099339

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For certain pointwise dual ergodic transformations we prove almost sure convergence of the log-averages

**[1]**Jon Aaronson,*Ergodic theory for inner functions of the upper half plane*, Ann. Inst. H. Poincaré Sect. B (N.S.)**14**(1978), no. 3, 233–253 (English, with French summary). MR**508928****[2]**Jon Aaronson,*The asymptotic distributional behaviour of transformations preserving infinite measures*, J. Analyse Math.**39**(1981), 203–234. MR**632462**, https://doi.org/10.1007/BF02803336**[3]**Jon. Aaronson,*Random 𝑓-expansions*, Ann. Probab.**14**(1986), no. 3, 1037–1057. MR**841603****[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).**[5]**K. L. Chung and P. Erdös,*Probability limit theorems assuming only the first moment. I*, Mem. Amer. Math. Soc.,**No. 6**(1951), 19. MR**0040612****[6]**William Feller,*An introduction to probability theory and its applications. Vol. II.*, Second edition, John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR**0270403****[7]**A. M. Fisher,*A pathwise central limit theorem for random walks*, Ann. Prob. (to appear).**[8]**-,*Integer Cantor sets and an order-two ergodic theorem*, J. D'Analyse Math. (to appear).**[9]**Gérard Letac,*Which functions preserve Cauchy laws?*, Proc. Amer. Math. Soc.**67**(1977), no. 2, 277–286. MR**0584393**, https://doi.org/10.1090/S0002-9939-1977-0584393-8**[10]**Maximilian Thaler,*Transformations on [0,1] with infinite invariant measures*, Israel J. Math.**46**(1983), no. 1-2, 67–96. MR**727023**, https://doi.org/10.1007/BF02760623

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
28D05,
60F15

Retrieve articles in all journals with MSC: 28D05, 60F15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1099339-4

Article copyright:
© Copyright 1992
American Mathematical Society