2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59596The Rademacher series in rearrangement invariant function spaces "closed" to the space L_\infty are considered. In terms of interpolation theory of operators a correspondence between such spaces and spaces of coefficients generated by them is stated. It is proved that this correspondence is one-to-one. Some examples and applications are presented.15 pagesFunctional AnalysisClassical Analysis and ODEs46B70 (primary), 46B40,42A55 (secondary)text