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The Rademacher series in rearrangement invariant function spaces close to the space L∞ are considered. In terms ofinterpolation theory of operators, a correspondence between suchspaces and spaces of coefficients generated by them is stated. Itis proved that this correspondence is one-to-one. Some examplesand applications are presented

About interpolation of subspaces of rearrangement invariant spaces generated by Rademacher system