A simpler proof is given for the recent result of I. Labuda and the author that a series in the space L0 (lambda) is subseries convergent if each of its lacunary subseries converges.
@article{urn:eudml:doc:44379,
title = {Lacunary convergence of series in L0 revisited.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {13},
year = {2000},
pages = {111-115},
zbl = {0981.46030},
mrnumber = {MR1794905},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44379}
}
Drewnowski, Lech. Lacunary convergence of series in L0 revisited.. Revista Matemática de la Universidad Complutense de Madrid, Tome 13 (2000) pp. 111-115. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44379/