Large structures made of nowhere $L^q$ functions

Szymon Głąb, Pedro L. Kaufmann, and Leonardo Pellegrini. "Large structures made of nowhere $L^{q}$ functions." Studia Mathematica 221.1 (2014): 13-34. <http://eudml.org/doc/285896>.

@article{SzymonGłąb2014,
abstract = {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 $f|_U$ is not in $L^\{q\}(U)$. 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.},
author = {Szymon Głąb, Pedro L. Kaufmann, Leonardo Pellegrini},
journal = {Studia Mathematica},
keywords = {nowhere functions; lineability; spaceability; algebrability},
language = {eng},
number = {1},
pages = {13-34},
title = {Large structures made of nowhere $L^\{q\}$ functions},
url = {http://eudml.org/doc/285896},
volume = {221},
year = {2014},
}

TY - JOUR
AU - Szymon Głąb
AU - Pedro L. Kaufmann
AU - Leonardo Pellegrini
TI - Large structures made of nowhere $L^{q}$ functions
JO - Studia Mathematica
PY - 2014
VL - 221
IS - 1
SP - 13
EP - 34
AB - 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 $f|_U$ is not in $L^{q}(U)$. 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.
LA - eng
KW - nowhere functions; lineability; spaceability; algebrability
UR - http://eudml.org/doc/285896
ER -