Quasi-measures with image transformations as generalized variables
type: Item
instance of: scholarly article
title: Quasi-measures with image transformations as generalized variables
zbMATH Open document ID: 1078.28010
DOI: 10.1016/S0022-247X(02)00076-8
author: Alf B. Rustad
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: The author introduces the notion of an image transformation and studies its properties to investigate whether the quasi-probability constructed by an image transformation could serve as a model for median and sample median in probability theory. In Section~2, it is shown that an image transformation naturally induces a mapping from probability measures into quasi-probability measures. In Section~3, a structure theorem for image transformations is given and as its consequence it is proved that image transformations defined only on solid sets extend uniquely to image transformations on all open or closed sets. In Section~4, the multidimensional median and sample median are presented as image transformations. Preservation (equivariance in statistical literature) properties of the medians are also given.
reviewed by: Jun Kawabe
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 28A10
zbMATH DE Number: 1836736
zbMATH Keywords: quasi-measure
zbMATH Keywords: image transformation
zbMATH Keywords: generalized variable
zbMATH Keywords: \(q\)-function
zbMATH Keywords: quasi-probability
MaRDI profile type: Publication
cites work: Quasi-states and quasi-measures
cites work: Transformations of states in operator theory and dynamics
cites work: Additivity of quasi-measures
cites work: Topological measures, image transformations and self-similar sets
cites work: Probability and quasi-measures - a new interpretation
cites work: Construction of non-subadditive measures and discretization of Borel measures
cites work: Topology and the construction of extreme quasi-measures
cites work: Unbounded quasi-integrals
cites work: Quasi-measures on completely regular spaces
cites work: Pure quasi-states and extremal quasi-measures
cites work: Spaces of Quasi-Measures
cites work: Q5585437
cites work: Q4043738
cites work: Physical States on a C ∗ -Algebra
cites work: Quasi-measures and dimension theory
full work available at URL: s0022-247x(02)00076-8
OpenAlex ID: W2077240130
description: scientific article; zbMATH DE number 1836736