Advanced Integration Theory

1. Front Matter

   Pages i-x

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2. Introduction

   • Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag

   Pages 1-4

3. Suggestions to the Reader

   • Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag

   Pages 5-6

4. Preliminaries

   • Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag

   Pages 7-20

5. Vector Lattices

   • Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag

   Pages 21-278

6. Elementary Integration Theory

   • Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag

   Pages 279-445

7. L^p-Spaces

   • Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag

   Pages 447-548

8. Real Measures

   • Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag

   Pages 549-636

9. The Radon-Nikodym Theorem. Duality

   • Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag

   Pages 637-679

10. The Classical Theory of Real Functions

    • Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag

    Pages 681-804

11. Back Matter

    Pages 805-870

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Since about 1915 integration theory has consisted of two separate branches: the abstract theory required by probabilists and the theory, preferred by analysts, that combines integration and topology. As long as the underlying topological space is reasonably nice (e.g., locally compact with countable basis) the abstract theory and the topological theory yield the same results, but for more compli­ cated spaces the topological theory gives stronger results than those provided by the abstract theory. The possibility of resolving this split fascinated us, and it was one of the reasons for writing this book. The unification of the abstract theory and the topological theory is achieved by using new definitions in the abstract theory. The integral in this book is de­ fined in such a way that it coincides in the case of Radon measures on Hausdorff spaces with the usual definition in the literature. As a consequence, our integral can differ in the classical case. Our integral, however, is more inclusive. It was defined in the book "C. Constantinescu and K. Weber (in collaboration with A.

• Lattice
• Probability theory
• integral transform
• measure
• real analysis

• Department of Mathematics, ETH-Zürich, Zürich, Switzerland

  Corneliu Constantinescu

• Department of Mathematics, Faculty of Engineering, Università di Palermo, Palermo, Italy

  Wolfgang Filter

• Technikum Winterthur, Winterthur, Switzerland

  Karl Weber

• Department of Mathematics, Wellesley College, Wellesley, USA

  Alexia Sontag

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