Infinite dimensional analysis. A hitchhiker's guide
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.
scientific article; zbMATH DE number 811063