Large structures made of nowhere functions
Volume 221 / 2014
Studia Mathematica 221 (2014), 13-34
MSC: Primary 46E30; Secondary 15A03.
DOI: 10.4064/sm221-1-2
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,\mu ) 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< \infty ) 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.
