1st Edition

Integration Theory

By Wolfgang Filter, K. Weber Copyright 1997
    296 Pages
    by Chapman & Hall

    This introductory text acts as a singular resource for undergraduates learning the fundamental principles and applications of integration theory.
    Chapters discuss: function spaces and functionals, extension of Daniell spaces, measures of Hausdorff spaces, spaces of measures, elements of the theory of real functions on R.

    Function Spaces and Functionals
    Ordered Sets, Lattices
    The Spaces RX and R-X
    Vector Lattices of Functions
    Daniell Spaces
    The Extension of Daniell Spaces
    Upper Functions
    Lower Functions
    The Closure of (x, L, I)
    Convergence of Theorems in (x, L(L), I)
    Null Functions and Null Sets, Integrability
    The Induction Principle
    Measure and Integral
    The Extension of Positive Measure Spaces
    Locally Integrable Functions
    Product Measures
    Fubini's Theorem
    Measures of Hausdorff Spaces
    Vector Lattices, Lp-Spaces
    Spaces of Measures
    The Vector Lattice Structure
    The Variation
    Hahn's Theorem
    Absolute Continuity
    The Radon-Nikodym Theorem
    Elements of the Theory of Real Functions on R
    Functions of Locally Finite Variation
    Absolutely Continuous Functions


    W. Filter Professor of Analysis University of Palermo Italy. K. Weber Professor of Mathematics Technikum Winterthur Switzerland.