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Table of Contents

I Sets.- II Topological Spaces.- III Continuous Functions on Compact Sets.- IV Banach Spaces.- V Hilbert Space.- VI The General Integral.- VII Duality and Representation Theorems.- VIII Some Applications of Integration.- IX Integration and Measures on Locally Compact Spaces.- X Riemann-Stieltjes Integral and Measure.- XI Distributions.- XII Integration on Locally Compact Groups.- XIII Differential Calculus.- XIV Inverse Mappings and Differential Equations.- XV The Open Mapping Theorem, Factor Spaces, and Duality.- XVI The Spectrum.- XVII Compact and Fredholm Operators.- XVIII Spectral Theorem for Bounded Hermltian Operators.- XIX Further Spectral Theorems.- XX Spectral Measures.- XXI Local Integration off Differential Forms.- XXII Manifolds.- XXIII Integration and Measures on Manifolds.- Table of Notation.