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arXiv · 1110.5774

Spaceability of sets of nowhere $L^q$ functions

Pedro L. Kaufmann·Leonardo Pellegrini
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Abstract

We say that a function $f:[0,1]\rightarrow \R$ is \emph{nowhere $L^q$} if, for each nonvoid open subset $U$ of $[0,1]$, the restriction $f|_U$ is not in $L^q(U)$. For a fixed $1 \leq p <\infty$, we will show that the set $$ S_p\doteq {f \in L^p[0,1]: f is nowhere $L^q$, for each p p} L_q[0,1]$ is spaceable for every $p>0$, preprint, 2011., since $S_p$ turns out to be spaceable. In addition, our result is a generalization of one of the main results from S. Głcab, P. L. Kaufmann, and L. Pellegrini, Spaceability and algebrability of sets of nowhere integrable functions, preprint, 2011.

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Pedro L. Kaufmann, Leonardo Pellegrini. 2011-10-26. Spaceability of sets of nowhere $L^q$ functions. https://arxiv.org/abs/1110.5774

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