We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and μ is a Borel measure on X with appropriate properties.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-5,
author = {Luis Bernal-Gonz\'alez},
title = {Algebraic genericity of strict-order integrability},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {279-293},
zbl = {1232.46026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-5}
}
Luis Bernal-González. Algebraic genericity of strict-order integrability. Studia Mathematica, Tome 196 (2010) pp. 279-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-5/