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TV1979A - 215 LETTERS TO THE EDITOR Theorem The following...

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LETTERS TO THE EDITOR 215 Theorem. The following three assertions are equivalent. (1) The collection Tk;i} forms a basis of decomposition which are e mod 0. (2) The S-code A {Ai} covers the Bernoulli scheme (Xz, Izp, T), or does not cover it, but the alphabet Z contains a letter ak such that almost every realization can be represented (uniquely up to an indexing ]l, a possible shift) in the form akBi_.ak akBi_..,ak akBjoak Bj, akBn,ak "’’, where Bi, -o< < o, is a word of any kind; i.e. all "lacunae" between words of whatever kind (for some there may be none) are filled by letters ak in arbitrary number. (3) For all letters aj Z, except possibly one (the ak in 2)), P(ai) ktloA’l-’lzp(.,), where to is the smallest positive real zero of the polynomial (series) ](t) l- + Zlzo(Ai)t la’l. The equality to (1 -Y./zp (/i)) -1 holds, in which the summation ranges over all words of any kind. There is coverability when all equalities in (3) are satisfied for all a..
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