A new set of sufficient conditions under which every sequence of independent identically distributed functions from a rearrangement invariant (r.i.) space on [0,1] spans there a Hilbertian subspace are given. We apply these results to resolve open problems of N. L. Carothers and S. L. Dilworth, and of M. Sh. Braverman, concerning such sequences in concrete r.i. spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-1,
author = {S. V. Astashkin and F. A. Sukochev},
title = {Sequences of independent identically distributed functions in rearrangement invariant spaces},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {27-37},
zbl = {1144.46025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-1}
}
S. V. Astashkin; F. A. Sukochev. Sequences of independent identically distributed functions in rearrangement invariant spaces. Banach Center Publications, Tome 83 (2008) pp. 27-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-1/