On products of admissible liftings and densities
type: Item
instance of: scholarly article
title: On products of admissible liftings and densities
zbMATH Open document ID: 0947.28005
DOI: 10.4171/ZAA/904
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2000-11-01T00:00:00Z
full work available at URL: https://eudml.org/doc/48546
review text: In Section 2, the class of admissible densities is introduced and studied. The main result in that section, Theorem 2.5, states that if \(\{(\Omega_i,\Sigma _i,\mu_i)\}_{i\in I}\) is a family of probability spaces with product \((\Omega,\Sigma,\mu)\), then for any fixed \(i_0\in I\) and for each density \(\tau _{i_0}\) (on \((\Omega,\Sigma,\mu_{i_0})\)) and for arbitrary admissible density \(\tau_i\) (on \((\Omega,\Sigma,\mu_i)\)) with \(i\in I\setminus \{i_{0}\}\) there exists a density \(\varphi\) (on \((\Omega,\Sigma,\mu)\)) such that \(\varphi\) respects coordinates, and \(\varphi\in\otimes_{i_0\in I}\tau_i\). This statement improves the corresponding result for product densities of \textit{N. D. Macheras} and \textit{W. Strauss} [Z. Anal. Anwend. 14, No. 1, 25-32 (1995; Zbl 0816.28006)] and implies the D. H. Fremlin's existence results for densities respecting coordinates. In Section 3, the class of admissibly generated liftings is introduced. This class let the authors to improve several results on product liftings and liftings respecting coordinates and also to provide them a unifying approach.
Mathematics Subject Classification ID: 28A51
Mathematics Subject Classification ID: 60A10
zbMATH DE Number: 1356401
zbMATH Keywords: Ybl 816.28006
zbMATH Keywords: densities
zbMATH Keywords: product liftings
author: Nikolaos Demetrios Macheras
author: Kazimierz Musial
author: Werner Strauß
reviewed by: P. Jiménez Guerra
MaRDI profile type: Publication
cites work: Q5182141
cites work: Q4112959
cites work: Q5509729
cites work: Strong liftings with application to measurable cross sections in locally compact groups
cites work: On strong liftings for projective limits
cites work: The product-lifting for arbitrary products of complete probability spaces
cites work: Products of lower densities
cites work: Closed convex hull of sets of measurable functions, Riemann measurable functions and measurability of translations
cites work: Pettis integral and measure theory
cites work: On liftings and the regularization of stochastic processes
OpenAlex ID: W2059556626
Recommended article: Splitting of liftings in products of probability spaces.
Recommended article: Q4523071
Recommended article: Various products for Lebesgue densities
Recommended article: Linear liftings respecting coordinates
Recommended article: Q5698945
Recommended article: Category product densities and liftings
Recommended article: The product-lifting for arbitrary products of complete probability spaces
Recommended article: Marginals and the product strong lifting problem
Recommended article: Q4802650
Recommended article: Q5489624
description: scientific article; zbMATH DE number 1356401