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The Rademacher sums are investigated in the BMO space on [0,1]. They span an uncomplemented subspace, in contrast to the dyadic space on [0,1], where they span a complemented subspace isomorphic to l₂. Moreover, structural properties of infinite-dimensional closed subspaces of the span of the Rademacher functions in BMO are studied and an analog of the Kadec-Pełczyński type alternative with l₂ and c₀ spaces is proved.
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