rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Nonstandard Analysis
  name:
    name part: Väth, Martin.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 252 p. online resource.
  abstract: Nonstandard analysis was originally developed by Robinson to rigorously justify infinitesimals like df and dx in expressions like df/dx in Leibniz' calculus or even to justify concepts like \delta-`functions'. However, the approach is much more general and was soon extended by Henson, Luxemburg and others to a useful tool especially in more advanced analysis, topology, and functional analysis. The book is an introduction with emphasis on those more advanced applications in analysis which are hardly accessible by other methods. Examples of such topics are a deeper analysis of certain functionals like Hahn-Banach limits or of finitely additive measures: From the viewpoint of classical analysis these are strange objects whose mere existence is even hard to prove. From the viewpoint of nonstandard analysis, these are rather 'explicit' objects. Formally, nonstandard analysis is an application of model theory in analysis. However, the reader of the book is not expected to have any background in model theory; instead knowledge of calculus is required and, although the book is rather self-contained, background in more advanced analysis or (elementary) topology is useful.
  table of contents: Preliminaries -- Nonstandard Models -- Nonstandard Real Analysis -- Enlargements and Saturated Models -- Functionals, Generalized Limits, and Additive Measures -- Nonstandard Topology and Functional Analysis -- Miscellaneous.
  note: by Martin Väth.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Mathematics
  subject:
    topic: Analysis
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783764377748
  identifier: http://dx.doi.org/10.1007/978-3-7643-7774-8
  record info:
    record creation date: 100301
    record change date: 20151204152951.0
    record identifier: 978-3-7643-7774-8