NDLI: A Note on the Ergodic Theorem

Content Provider	Springer Nature Link
Author	Carvalho, Maria Pires Moreira, Fernando Jorge
Copyright Year	2014
Abstract	Given a space $$X$$ , a $$\sigma $$ -algebra $$\mathfrak {B}$$ on $$X$$ and a measurable map $$T:X \rightarrow X$$ , we say that a measure $$\mu $$ is half-invariant by $$T$$ if, for any $$B \in \mathfrak {B}$$ , we have $$\mu \left( T^{-1}(B)\right) \le \mu (B)$$ . We will present a generalization of Birkhoff ergodic theorem to $$\sigma $$ -finite half-invariant measures.
Starting Page	253
Ending Page	268
Page Count	16
File Format	PDF
ISSN	15755460
Journal	Qualitative Theory of Dynamical Systems
Volume Number	13
Issue Number	2
e-ISSN	16623592
Language	English
Publisher	Springer Basel
Publisher Date	2014-06-11
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Birkhoff’s averages Pointwise convergence Ergodic theorems, spectral theory, Markov operators Mathematics Dynamical Systems and Ergodic Theory Difference and Functional Equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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A Note on the Ergodic Theorem