296 Pages
by
Chapman & Hall
296 Pages
by
Routledge
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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.
Introduction
Function Spaces and Functionals
Ordered Sets, Lattices
The Spaces RX and R-X
Vector Lattices of Functions
Functionals
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)
Examples
Null Functions and Null Sets, Integrability
Examples
The Induction Principle
Summary
Measure and Integral
The Extension of Positive Measure Spaces
Examples
Locally Integrable Functions
Product Measures
Fubini's Theorem
Measures of Hausdorff Spaces
Lp-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
Function Spaces and Functionals
Ordered Sets, Lattices
The Spaces RX and R-X
Vector Lattices of Functions
Functionals
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)
Examples
Null Functions and Null Sets, Integrability
Examples
The Induction Principle
Summary
Measure and Integral
The Extension of Positive Measure Spaces
Examples
Locally Integrable Functions
Product Measures
Fubini's Theorem
Measures of Hausdorff Spaces
Lp-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
