Real Analysis Exchange

Superporosity in a class of non-normable spaces

László Zsilinszky

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Abstract

Let \(\mathcal M\) stand for the space of all \(S\)-measurable real functions on the infinite \(\sigma\)-finite measure space \((X,S,\mu)\) endowed with the (metrizable but non-normable) topology of convergence in measure on sets of finite measure. Some natural subsets (including the \(L_p\)-spaces) are proved to be sigma-superporous in \(\mathcal M\). The possibility of finding non-sigma-porous meager sets in this non-normable setting is discussed.

Article information

Source
Real Anal. Exchange, Volume 22, Number 2 (1996), 785-797.

Dates
First available in Project Euclid: 22 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1337713158

Mathematical Reviews number (MathSciNet)
MR1460989

Zentralblatt MATH identifier
0943.28004

Subjects
Primary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence

Keywords
superporosity non-normable

Citation

Zsilinszky, László. Superporosity in a class of non-normable spaces. Real Anal. Exchange 22 (1996), no. 2, 785--797. https://projecteuclid.org/euclid.rae/1337713158


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