Real Analysis Exchange

On Completeness Generated by Convergence with Respect to a σ-Ideal

Marek Balcerzak

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Abstract

We consider convergence (introduced by E. Wagner in 1981) with respect to a $\sigma$-ideal of $\mathscr{S}$-measurable real valued functions on $Y$ where $\mathscr{S}\subset \mathscr{P} (Y)$ is a $\sigma$-algebra containing a given $\sigma$-ideal $\mathscr{J}$. We check which operations preserve completeness generated by convergence with respect to a $\sigma$-ideal. We introduce uniform kinds of $\mathscr{J}$-convergence and $\mathscr{J}$-completeness and use them in a statement concerning the Fubini product of two $\sigma$-ideals.

Article information

Source
Real Anal. Exchange, Volume 32, Number 2 (2006), 473-488.

Dates
First available in Project Euclid: 3 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1199377484

Mathematical Reviews number (MathSciNet)
MR2369856

Zentralblatt MATH identifier
1135.28003

Subjects
Primary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 40A30: Convergence and divergence of series and sequences of functions

Keywords
convergence of measurable functions $\sigma$-ideal $\J$-completenes

Citation

Balcerzak, Marek. On Completeness Generated by Convergence with Respect to a σ-Ideal. Real Anal. Exchange 32 (2006), no. 2, 473--488. https://projecteuclid.org/euclid.rae/1199377484


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