Infinite dimensional analysis. A hitchhiker's guide
type: Item
instance of: scholarly article
title: Infinite dimensional analysis. A hitchhiker's guide
zbMATH Open document ID: 0839.46001
author: Kim C. Border
author: Charalambos D. Aliprantis
published in: Studies in Economic Theory
publication date: 1995-10-30T00:00:00Z
review text: The book is an excellent overview of the main results in infinite-dimensional analysis which may be applicable to economical problems. Infinite-dimensional models have become prominent in economics and finance because they capture natural aspects of the world that cannot be described and examined in finite-dimensional models. Dynamic models require infinite-dimensional function spaces. Another feature of the world that arguably requires infinite-dimensional modeling is uncertainty. The approach used in the book is very modern and rigorous. The choice of the subjects is of course open to discussion, but from the reviewer's point of view it has been made very successfully. The content can be estimated from the list of chapter titles: Odds and ends. Topology. Metrizable spaces. Topological vector spaces. Normed spaces. Riesz spaces. Banach lattices. Charges and Measures. Integrals. \(L_p\)-spaces. Measures and topology. Probability measures on metrizable spaces. Spaces of sequences. Correspondences. Markov transitions. Ergodicity.
Mathematics Subject Classification ID: 46-01
Mathematics Subject Classification ID: 46N10
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 811063
zbMATH Keywords: function spaces
zbMATH Keywords: charges
zbMATH Keywords: measures
zbMATH Keywords: integrals
zbMATH Keywords: ergodicity
zbMATH Keywords: dynamic models
zbMATH Keywords: infinite-dimensional analysis
zbMATH Keywords: economical problems
zbMATH Keywords: uncertainty
zbMATH Keywords: Riesz spaces
zbMATH Keywords: Banach lattices
zbMATH Keywords: Markov transitions
reviewed by: Jiří Vaníček
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 811063