A Class of Weak Bernoulli Transformations Associated with Representations of Real Numbers | Zendy

Alufohai Imohimi C. | Zendy

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A Class of Weak Bernoulli Transformations Associated with Representations of Real Numbers

Author(s) -

Alufohai Imohimi C.

Publication year - 1981

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/s2-23.2.295

Subject(s) - citation , class (philosophy) , bernoulli's principle , mathematics , computer science , mathematics education , combinatorics , library science , artificial intelligence , engineering , aerospace engineering

A class W of transformations which are usually associated with representations of real numbers is considered. We prove that every T e W is weak Bernoulli. Our proof is based on Doeblin (1), Rudolfer and Wilkinson (5). Several authors (1), (2), (4), (5), (6), (7), (8), (9) have studied ergodic properties of many number- theoretical transformations but all assumed that proper atoms existed and that the improper ones could be 'approximated' by the proper ones. Our class W includes this case and not only that: it also includes the case when only improper atoms exist. Our only requirement is that T should have property (e). Both the transformation

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