Assume that Lp,q, Lp1, q1,..., LLpn, qn are Lorentz spaces. This article studies the question: what is the size of the set We prove the following dichotomy: either E =Lp1, q1× ... × Lpn, qn or E is σ-porous in Lp1, q1× ... × Lpn, qn, provided 1/p ≠ 1/p1 + ... + 1/pn. In general case we obtain that either E = Lp1, q1× ... × Lpn, qn or E is meager. This is a generalization of the results for classical Lp spaces.
|Number of pages||15|
|Journal||Central European Journal of Mathematics|
|Publication status||Published - 2013|
- Baire category
- Lorentz spaces
ASJC Scopus subject areas