Journal
STUDIA MATHEMATICA
Volume 221, Issue 1, Pages 13-34Publisher
POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN
DOI: 10.4064/sm221-1-2
Keywords
nowhere L-q functions; spaceability; algebrability; lineability
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Funding
- National Science Centre of Poland [DEC-2012/07/D/ST1/02087]
- CAPES [PNPD 2256-2009, BEX 10057/12-9]
- Laboratoire d'Analyse Fonctionnelle of the Institut de Mathematiques de Jussieu
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We say that a real-valued function f defined on a positive Borel measure space (X, mu) is nowhere q-integrable if, for each nonvoid open subset U of X, the restriction flu is not in L-q(U). When (X, mu) has some natural properties, we show that certain sets of functions defined in X which are p-integrable for some p's but nowhere q-integrable for some other q's (0 < p, q < infinity) admit a variety of large linear and algebraic structures within them. The presented results answer a question of Bernal-Gonzalez, improve and complement recent spaceability and algebrability results of several authors and motivate new research directions in the field of spaceability.
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