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Large structures made of nowhere $L^{q}$ functions

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Głąb S., Kaufmann P., Pellegrini L.

Studia Mathematica

2014

tom 221

nr 1

13-34

We say that a real-valued function f defined on a positive Borel measure space (X,μ) is nowhere q-integrable if, for each nonvoid open subset U of X, the restriction $f|_U$ is not in $L^{q}(U)$. When (X,μ) 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 < ∞) admit a variety of large linear and algebraic structures within them. The presented results answer a question of Bernal-González, improve and complement recent spaceability and algebrability results of several authors and motivate new research directions in the field of spaceability.

Ograniczanie wyników

1 Studia Mathematica

1 Głąb S.

1 Kaufmann P.

1 Pellegrini L.

1 2014

Wyniki wyszukiwania

Large structures made of nowhere $L^{q}$ functions