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

N. D. Macheras, K. MusiaŁ, and W. Strauss
Source: Real Anal. Exchange Volume 29, Number 1 (2003), 473-480.

#### 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.

First Page:
Primary Subjects: 28A51
Secondary Subjects: 28A35, 28E15
Full-text: Open access