Real Analysis Exchange

Non-existence of certain types of liftings and densities in product spaces with σ-ideals.

N. D. Macheras, K. MusiaŁ, and W. Strauss

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Abstract

We prove that if $(\Omega,\Sigma,\mathcal{I}),\; (\Theta,T,\mathcal{J})$ and $(\Omega \times\Theta,\Xi,\mathcal{K})$ are measurable spaces with $\sigma$-ideals satisfying some natural Fubini type conditions then there is no density on $(\Omega\times\Theta,\Xi,\mathcal{K})$ with density invariant sections.

Article information

Source
Real Anal. Exchange, Volume 29, Number 1 (2003), 473-480.

Dates
First available in Project Euclid: 9 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149860219

Mathematical Reviews number (MathSciNet)
MR2063088

Zentralblatt MATH identifier
1096.28002

Subjects
Primary: 28A51: Lifting theory [See also 46G15]
Secondary: 28A35: Measures and integrals in product spaces 28E15: Other connections with logic and set theory

Keywords
liftings product liftings $\sigma$-ideals product measures densities product densities

Citation

Strauss, W.; Macheras, N. D.; MusiaŁ, K. Non-existence of certain types of liftings and densities in product spaces with σ-ideals. Real Anal. Exchange 29 (2003), no. 1, 473--480. https://projecteuclid.org/euclid.rae/1149860219


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