We say that a real-valued function f defined on a positive Borel measure space (X,μ) is nowhere q-integrable if, for each nonvoid open subset U of X, the restriction is not in . When (X,μ) has some natural properties, we show that certain sets of functions defined in X which are p-integrable for some p’s but nowhere q-integrable for some other q’s (0 < p,q < ∞) admit a variety of large linear and algebraic structures within them. The presented results answer a question of Bernal-González, improve and complement recent spaceability and algebrability results of several authors and motivate new research directions in the field of spaceability.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-1-2,
author = {Szymon G\l \k ab and Pedro L. Kaufmann and Leonardo Pellegrini},
title = {Large structures made of nowhere $L^{q}$ functions},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {13-34},
zbl = {1314.46034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-1-2}
}
Szymon Głąb; Pedro L. Kaufmann; Leonardo Pellegrini. Large structures made of nowhere $L^{q}$ functions. Studia Mathematica, Tome 223 (2014) pp. 13-34. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm221-1-2/