TV1979A - LETTERS T O THE EDITOR 215 Theorem. The...

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Unformatted text preview: LETTERS T O THE EDITOR 215 Theorem. The followingthreeassertionsare equivalent. (1) The collection Tk;i} forms a basis of decomposition which aree mod 0. (2) TheS-codeA {Ai}coverstheBernoullischeme (Xz, Izp, T),ordoesnotcoverit,but the alphabetZ contains a letter ak such that almost every realization can be represented (uniquelyup toan indexing]l,a possibleshift)in the form akBi_.ak akBi_..,ak akBjoak Bj, akBn,ak"’’, whereBi,-o< < o, isa word of any kind; i.e.all"lacunae" between words of whatever kind (for some theremay benone)are filled by letters ak in arbitrary number. (3) Foralllettersaj Z,exceptpossiblyone (the ak in 2)), P(ai) ktloA’l-’lzp(.,), where to isthe smallestpositiverealzero of thepolynomial (series) ](t) l- +Zlzo(Ai)t la’l. The equality to (1-Y./zp (/i))-1 holds,inwhich thesummation rangesover allwords ofanykind.Thereiscoverabilitywhen allequalitiesin(3)aresatisfiedforall a.....
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This note was uploaded on 12/06/2011 for the course MATH 101 taught by Professor Eugenea.feinberg during the Fall '11 term at State University of New York.

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