Algebraic genericity of strict-order integrability

Luis Bernal-González. "Algebraic genericity of strict-order integrability." Studia Mathematica 199.3 (2010): 279-293. <http://eudml.org/doc/285468>.

@article{LuisBernal2010,
abstract = {We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space $L^\{p\}(μ,X)$ (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of $L^\{p\}(μ,X)$ (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and μ is a Borel measure on X with appropriate properties.},
author = {Luis Bernal-González},
journal = {Studia Mathematica},
keywords = {dense lineability; maximal lineability; Lebesgue space},
language = {eng},
number = {3},
pages = {279-293},
title = {Algebraic genericity of strict-order integrability},
url = {http://eudml.org/doc/285468},
volume = {199},
year = {2010},
}

TY - JOUR
AU - Luis Bernal-González
TI - Algebraic genericity of strict-order integrability
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 3
SP - 279
EP - 293
AB - We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space $L^{p}(μ,X)$ (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of $L^{p}(μ,X)$ (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and μ is a Borel measure on X with appropriate properties.
LA - eng
KW - dense lineability; maximal lineability; Lebesgue space
UR - http://eudml.org/doc/285468
ER -