Hopf's ratio ergodic theorem by inducing
نویسندگان
چکیده
منابع مشابه
On the ratio ergodic theorem for group actions
We study the ratio ergodic theorem (RET) of Hopf for group actions. Under a certain technical condition, if a sequence of sets {Fn} in a group satisfy the RET, then there is a finite set E such that {EFn} satisfies the Besicovitch covering property. Consequently for the abelian group G = ⊕n=1Z there is no sequence Fn ⊆ G along which the RET holds, and in many finitely generated groups, includin...
متن کاملA Ratio Ergodic Theorem for Multiparameter Non-singular Actions
We prove a ratio ergodic theorem for non-singular free Z and R actions, along balls in an arbitrary norm. Using a Chacon-Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in R. The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact tha...
متن کاملKingman's Subadditive Ergodic Theorem Kingman's Subadditive Ergodic Theorem
A simple proof of Kingman’s subadditive ergodic theorem is developed from a point of view which is conceptually algorithmic and which does not rely on either a maximal inequality or a combinatorial Riesz lemma.
متن کاملErgodic theorem, ergodic theory, and statistical mechanics.
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...
متن کاملA Marginal Ergodic Theorem
Michael Lavine Duke University, Durham, NC, USA. Summary. In recent years there have been several papers giving examples of Markov Chain Monte Carlo (MCMC) algorithms whose invariant measures are improper (have infinite mass) and which therefore are not positive recurrent, yet which have subchains from which valid inference can be derived. These are nonergodic (not having a limiting distributio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2004
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm101-2-11