Abstract
For spaces of random variables with martingale mixed norm the theorem of A. Pelczynski on the absence of an unconditional basis in the space $$L_1(0,1)$$ is generalized and (in terms of summability exponents) the cases are studied when these spaces coincide with the space $$L_1$$ . 2020 Mathematics subject classification: Primary 60G46; Secondary 60G42, 46E30.
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