Mod 2 normal numbers and skew products

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dc.contributor.authorChoe, Geon Hoko
dc.contributor.authorHamachi, Tko
dc.contributor.authorNakada, Hko
dc.date.accessioned2013-03-04T04:18:56Z-
dc.date.available2013-03-04T04:18:56Z-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.issued2004-
dc.identifier.citationSTUDIA MATHEMATICA, v.165, no.1, pp.53 - 60-
dc.identifier.issn0039-3223-
dc.identifier.urihttp://hdl.handle.net/10203/81887-
dc.description.abstractLet E be an interval in the unit interval [0, 1). For each x is an element of [0, 1) define d(n)(x) is an element of {0, 1} by d(n)(x) := Sigma(i=1)(n) 1(E)({2(i-1)x}) (mod 2), where {t} is the fractional part of t. Then x is called a normal number mod 2 with respect to E if N-1 Sigma(n=1)(N) d(n)(x) converges to 1/2. It is shown that for any interval E not equal (1/6,5/6) a.e. x is a normal number mod 2 with respect to E. For E = (1/6,5/6) it is proved that N-1 Sigma(n=1)(N) d(n) (x) converges a.e. and the limit equals 1/3 or 2/3 depending on x.-
dc.languageEnglish-
dc.publisherPOLISH ACAD SCIENCES INST MATHEMATICS-
dc.subjectABSOLUTELY CONTINUOUS COCYCLES-
dc.subjectIRRATIONAL ROTATIONS-
dc.subjectSTRICT ERGODICITY-
dc.subjectSPECTRAL TYPES-
dc.subjectEXTENSIONS-
dc.subjectINTERVAL-
dc.titleMod 2 normal numbers and skew products-
dc.typeArticle-
dc.identifier.wosid000226240000004-
dc.identifier.scopusid2-s2.0-5644229918-
dc.type.rimsART-
dc.citation.volume165-
dc.citation.issue1-
dc.citation.beginningpage53-
dc.citation.endingpage60-
dc.citation.publicationnameSTUDIA MATHEMATICA-
dc.identifier.doi10.4064/sm165-1-4-
dc.contributor.localauthorChoe, Geon Ho-
dc.contributor.nonIdAuthorHamachi, T-
dc.contributor.nonIdAuthorNakada, H-
dc.type.journalArticleArticle-
dc.subject.keywordPlusABSOLUTELY CONTINUOUS COCYCLES-
dc.subject.keywordPlusIRRATIONAL ROTATIONS-
dc.subject.keywordPlusSTRICT ERGODICITY-
dc.subject.keywordPlusSPECTRAL TYPES-
dc.subject.keywordPlusEXTENSIONS-
dc.subject.keywordPlusINTERVAL-
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