Lineability of non-differentiable Pettis primitives

被引：3

作者：

Bongiorno, B. ^{[1
]}

Darji, U. B. ^{[2
]}

Di Piazza, L. ^{[1
]}

机构：

[1] Univ Palermo, Dept Math, I-90123 Palermo, Italy

[2] Univ Louisville, Dept Math, Louisville, KY 40292 USA

来源：

MONATSHEFTE FUR MATHEMATIK | 2015年 / 177卷 / 03期

关键词：

Pettis integral; Nowhere differentiable; Dvoretzky's theorem; Lineable; Spaceable; SPACEABILITY; SPACES; SETS; ALGEBRABILITY;

D O I：

10.1007/s00605-014-0703-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be an infinite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an -valued Pettis integrable function on whose primitive is nowhere weakly differentiable. Using their technique and some new ideas we show that , the set of strongly measurable Pettis integrable functions with nowhere weakly differentiable primitives, is lineable, i.e., there is an infinite dimensional vector space whose nonzero vectors belong to .

引用

页码：345 / 362

页数：18

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