This is an announcement for the paper "Large structures made of nowhere $L^p$ functions" by Szymon Glab, Pedro L. Kaufmann and Leonardo Pellegrini.

Abstract: We say that a real-valued function $f$ defined on a positive Borel measure space $(X,\mu)$ is nowhere $q$-integrable if, for each nonvoid open subset $U$ of $X$, the restriction $f|_U$ is not in $L^q(U)$. When $X$ is a Polish space and $\mu$ satisfies some natural properties, we show that certain sets of functions which are $p$-integrable for some $p$'s but nowhere $q$-integrable for some other $q$'s ($0<p,q<\infty$) admit large linear and algebraic structures within them. In our Polish space context, the presented results answer a question from Bernal-Gonz'alez [L. Bernal-Gonz'alez, Algebraic genericity and strict-order integrability, Studia Math. 199(3)(2010), 279--293], and improves and complements results of several authors.

Archive classification: math.FA

Submitted from: leoime@yahoo.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.3818

or

http://arXiv.org/abs/1207.3818