The ergodic infinite measure preserving transformation of boole

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1973 English Publisher:Springer Science and Business Media LLCJournal:Israel Journal of Mathematics, volume 16, pages 263-278 (issn: 0021-2172, eissn: 1565-8511,

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Authors: Adler, Roy. L.; Weiss, Benjamin;

doi: 10.1007/bf02756706

The ergodic infinite measure preserving transformation of boole

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Abstract

G. Boole proved that the transformation φ of the real line, defined by φ(x)=x−1/x, preserves Lebesgue measure. A general method is applied to proving that φ is ergodic. Some further applications of the method are also indicated.

Related Organizations

IBM (United States)
United States
Hebrew University of Jerusalem
Israel
IBM Research – Thomas J. Watson Research Center
United States

Keywords

One-variable calculus, Measure-preserving transformations, Rate of growth of functions, orders of infinity, slowly varying functions, Ergodic theory of linear operators

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