A note on the Kawada–Itô theorem

Heybetkulu Mustafayev

Statistics & Probability Letters, 2022, vol. 181, issue C

Abstract: A probability measure μ on a locally compact group G is said to be adapted if the support of μ generates a dense subgroup of G. A classical Kawada–Itô theorem asserts that if μ is an adapted measure on a compact metrizable group G, then the sequence of probability measures 1n∑k=0n−1μkn=1∞ weak∗ converges to the Haar measure on G. In this note, we present a new proof of Kawada–Itô theorem. Also, we show that metrizability condition in the Kawada–Itô theorem can be removed. Some applications are also given.

Keywords: Mean ergodic theorem; Locally compact group; Probability measure; Convergence (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715221002236
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:181:y:2022:i:c:s0167715221002236

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2021.109261

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().