학술논문
On the Spaceability of the Set of Functions in the Lebesgue Space Lp Which are Not in Lq.
Document Type
Article
Author
Source
Subject
Language
ISSN
1678-7544
Abstract
We answer an open problem posed by Fávaro, Pellegrino and Tomáz in (Bull Braz Math Soc 51:27–46, 2020b). Namely, we prove that, for all 0 < p < ∞ , the set L p [ 0 , 1 ] \ ⋃ q ∈ p , ∞ L q [ 0 , 1 ] is (α , c) -spaceable in L p [ 0 , 1 ] if, and only if, α < ℵ 0 . [ABSTRACT FROM AUTHOR]