Equimeasurable symmetric spaces of measurable function
Abstract
In this paper we consider equimeasurable symmetric(rearrangement invariant) spaces E1 = E1(1,F1,μ1) and E2 = E2(2,F2,μ2) on a measure spaces (1, F1,μ1) and (2,F2,μ2) with finite or infinite σ-finite non-atomic measures μ1 and μ2. If E1(1,F1,μ1) be a symmetric space on a measure spaces (1, F1,μ1) and (2,F2,μ2) be a measure space such that μ1 (1)=μ2(2), then there exists a unique symmetric space E2(2,F2,μ2) on (2,F2,μ2), which is equimeasurable to E1(1,F1,μ1).
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