rank1-zeroentr - Rank- 1 has zero entropy Jonathan L.F....

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Unformatted text preview: Rank- 1 has zero entropy Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA squash@math.ufl.edu Webpage http://www.math.ufl.edu/ squash/ 20 November, 2006 (at 18:39 ) Using stacks Let--- STKs := ( n ) n =1 be the stacks used to cut&stack a rank-1 T , on a non-atomic Lebesgue space ( X, X , ) . Let L n denote the height of n . Let S n X denote the spacers adjoined to make the n-stack. Thus n t S n +1 = n +1 . Let A n := F j = n +1 S j be the spacers adjoined a fter stage- n . Certainly ( A n ) & 0. I first construct a particular 2-set generating parti- tion P = ( B,G ) . Step 1. For ( n ) n =1 , I will DTASARenumber (Drop To A Subsequence And Renumber) several times, so as to gain a new property for--- STKs. Later subse- quencings will preserve the properties obtained ear- lier. I can initially DTASARenumber so that L n > n + 3, for all n ....
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This note was uploaded on 01/26/2012 for the course MTG 6401 taught by Professor Staff during the Fall '09 term at University of Florida.

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rank1-zeroentr - Rank- 1 has zero entropy Jonathan L.F....

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