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/