Lacunary convergence of series in 𝐿₀

Drewnowski, Lech; Labuda, Iwo

doi:10.1090/S0002-9939-98-04189-6

Lacunary convergence of series in $L_0$
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Proc. Amer. Math. Soc. 126 (1998), 1655-1659 Request permission

Abstract:

For a finite measure $\lambda$, let $L_{0}(\lambda )$ denote the space of $\lambda$-measurable functions equipped with the topology of convergence in measure. We prove that a series in $L_{0}(\lambda )$ is subseries (or unconditionally) convergent provided each of its lacunary subseries converges.

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