Spaceability of strict order integrability

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• 作者：Luis Bernal-Gonzá ; lez ; ^a ; ^{lbernal@us.es"" rel=""nofollow} ; Manuel Ord&#xf3 ; &#xf1 ; ez Cabrera^a ; ^{cabrera@us.es"" rel=""nofollow}
• 关键词：Lineability ; Spaceability ; Lebesgue space ; Strict order integrability ; Bounded variation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：1 January 2012
• 年：2012
• 卷：385
• 期：1
• 页码：303-309
• 全文大小：182 K

文摘

In this paper, sharp conditions on a measure space are provided in order that the subset of functions in the corresponding Lebesgue space L^p which are in no other L^q contains, except for zero, an infinite dimensional closed subspace. This completes earlier work of several authors. The main result is derived from a new, general criterion for spaceability on function spaces. A further application to spaceability of the class of non-absolutely continuous functions is supplied.