Algebraic genericity of strict-order integrability

被引：40

作者：

Bernal-Gonzalez, Luis ^{[1
]}

机构：

[1] Univ Seville, Fac Matemat, E-41080 Seville, Spain

来源：

STUDIA MATHEMATICA | 2010年 / 199卷 / 03期

关键词：

dense-lineability; maximal lineability; Lebesgue space; strict order of integration; Borel measure; FUNCTION-SPACES; LINEABILITY; ALGEBRABILITY; SPACEABILITY; SUBSETS; SETS;

D O I：

10.4064/sm199-3-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide sharp conditions on a measure mu defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space L(p)(mu, X) (p >= 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of LP(mu, X) (without zero). This improves recent results due to Aron, Garcia, Munoz, Palmberg, Perez, 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 mu is a Borel measure on X with appropriate properties.

引用

页码：279 / 293

页数：15

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