A Method of Averaging in the Theory of Orthogonal Series and Some Problems in the Theory of Bases, Issue 146

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American Mathematical Soc., 1980 - Mathematics - 92 pages
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Chapter I Averaging Over Independent Arrangements of Signs
Averaging Over Shifts and Singular Functions
Averaging Over Supports of 8 Functions
Chapter IV Some Problems in the Theory Bases

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Page 3 - This contradicts the fact that A is not a cylinder. The theorem is now proved. Naturally the question arises as to whether a non-recursive m-degree that is not indecomposable contains a countable number of pairwise incomparable 1 -degrees. For re m-degrees a positive answer to this question was obtained by the author in [4] . Here we give a more modest result illustrating the basic idea of the construction of such an antichain. THEOREM 2. If S is a re non-recursive set and not a cylinder, then sets...

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