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Rational countable steps functions on the circle and ergodicity of Maharam measures
Author(s) -
Brémont Julien
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt001
Subject(s) - mathematics , ergodicity , countable set , lebesgue integration , pure mathematics , skew , irrational number , lebesgue measure , bounded variation , measure (data warehouse) , series (stratigraphy) , bounded function , rotation number , discrete mathematics , rotation (mathematics) , mathematical analysis , statistics , geometry , paleontology , database , computer science , biology , physics , astronomy
We consider skew‐products defined by countable steps functions with rational endpoints and bounded variation (BV) over an irrational rotation on the circle. We study the ergodicity of the Lebesgue measure and more generally of all conformal (also called Maharam) measures. We next give an application to BV Davenport series.