Logo Oapen
  • Search
  • Join
    • Deposit
    • For Librarians
    • For Publishers
    • For Researchers
    • Funders
    • Resources
    • OAPEN
    • For Librarians
    • For Publishers
    • For Researchers
    • Funders
    • Resources
    • OAPEN
    View Item 
    •   OAPEN Home
    • View Item
    •   OAPEN Home
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Measure, Integration & Real Analysis

    Thumbnail
    Download PDF Viewer
    Web Shop
    Author(s)
    Axler, Sheldon
    Language
    English
    Show full item record
    Abstract
    This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.
    URI
    http://library.oapen.org/handle/20.500.12657/23111
    Keywords
    Mathematics; Measure theory; Textbook
    DOI
    10.1007/978-3-030-33143-6
    Publisher
    Springer Nature
    Publisher website
    https://www.springernature.com/gp/products/books
    Publication date and place
    Cham, 2020
    Series
    Graduate Texts in Mathematics,
    Classification
    Integral calculus and equations
    Pages
    411
    • Imported or submitted locally

    Browse

    All of OAPENSubjectsPublishersLanguagesCollections

    My Account

    LoginRegister

    Export

    Repository metadata
    Logo Oapen
    • For Librarians
    • For Publishers
    • For Researchers
    • Funders
    • Resources
    • OAPEN

    Newsletter

    • Subscribe to our newsletter
    • view our news archive

    Follow us on

    License

    • If not noted otherwise all contents are available under Attribution 4.0 International (CC BY 4.0)

    Credits

    • logo EU
    • This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 683680, 810640, 871069 and 964352.

    OAPEN is based in the Netherlands, with its registered office in the National Library in The Hague.

    Director: Niels Stern

    Address:
    OAPEN Foundation
    Prins Willem-Alexanderhof 5
    2595 BE The Hague
    Postal address:
    OAPEN Foundation
    P.O. Box 90407
    2509 LK The Hague

    Websites:
    OAPEN Home: www.oapen.org
    OAPEN Library: library.oapen.org
    DOAB: www.doabooks.org

     

     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Differen formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    A logged-in user can export up to 15000 items. If you're not logged in, you can export no more than 500 items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.