Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Upper bounds for ergodic sums of infinite measure preserving transformations


Authors: Jon Aaronson and Manfred Denker
Journal: Trans. Amer. Math. Soc. 319 (1990), 101-138
MSC: Primary 28D05; Secondary 60F15
MathSciNet review: 1024766
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For certain conservative, ergodic, infinite measure preserving transformations $ T$ we identify increasing functions $ A$, for which

$\displaystyle \limsup \limits_{n \to \infty } \frac{1} {{A(n)}}\sum\limits_{k = 1}^n {f \circ } {T^k} = \int_X {fd\mu } \quad {\text{a}}{\text{.e}}{\text{.}}$

holds for any nonnegative integrable function $ f$. In particular the results apply to some Markov shifts and number-theoretic transformations, and include the other law of the iterated logarithm.

References [Enhancements On Off] (What's this?)


Similar Articles

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

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


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-1024766-3
PII: S 0002-9947(1990)1024766-3
Article copyright: © Copyright 1990 American Mathematical Society