Tags
Language
Tags
June 2025
Su Mo Tu We Th Fr Sa
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 1 2 3 4 5
    Attention❗ To save your time, in order to download anything on this site, you must be registered 👉 HERE. If you do not have a registration yet, it is better to do it right away. ✌

    ( • )( • ) ( ͡⚆ ͜ʖ ͡⚆ ) (‿ˠ‿)
    SpicyMags.xyz

    Real Analysis

    Posted By: Underaglassmoon
    Real Analysis

    Real Analysis
    Birkhäuser | Mathematics | May 6 2016 | ISBN-10: 3319307428 | 274 pages | pdf | 2.67 mb

    Authors: Loeb, Peter A
    Written by one of the leading scholars in the field Includes a novel presentation of differentiation and absolute continuity using a local maximum function, resulting in an exposition that is both simpler and more general than the traditional approach
    Theorems are stated for Lebesgue and Borel measures, with a note indicating when the same proof works only for Lebesgue measures
    Appendices cover additional material, including theorems for higher dimensions and a short introduction to nonstandard analysis


    This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors.
    The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach.
    The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics.

    Topics
    Real Functions
    Functional Analysis
    Measure and Integration

    Click Here to Buy the Hardcover from Springer



    Click Here for More books