The averaging operator with respect to a countable partition on a minimal symmetric ideal of the space L1(0, 1)
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In terms of the functions f * and f** one gives necessary and sufficient conditions for the inclusion, where f is an arbitrary element from L1(0, 1), Nf is the smallest symmetric ideal in L1(0, 1), containing f, is a partition of the segment [0, 1] by the points of the sequence tn↓ 0, and is the mathematical expectation operator.
KeywordsAverage Operator Countable Partition Symmetric Ideal
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