Journal of Soviet Mathematics

, Volume 36, Issue 3, pp 382–391 | Cite as

The averaging operator with respect to a countable partition on a minimal symmetric ideal of the space L1(0, 1)

  • A. A. Mekler


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.


Average Operator Countable Partition Symmetric Ideal 


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Copyright information

© Plenum Publishing Corporation 1987

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  • A. A. Mekler

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