Advanced Integration Theory

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

Part of the Mathematics and Its Applications book series (MAIA, volume 454)

Table of contents

  1. Front Matter
    Pages i-x
  2. Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
    Pages 1-4
  3. Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
    Pages 5-6
  4. Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
    Pages 7-20
  5. Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
    Pages 21-278
  6. Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
    Pages 279-445
  7. Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
    Pages 447-548
  8. Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
    Pages 549-636
  9. Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
    Pages 637-679
  10. Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
    Pages 681-804
  11. Back Matter
    Pages 805-870

About this book

Introduction

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.

Keywords

Lattice Probability theory integral transform measure real analysis

Authors and affiliations

  • Corneliu Constantinescu
    • 1
  • Wolfgang Filter
    • 2
  • Karl Weber
    • 3
  • Alexia Sontag
    • 4
  1. 1.Department of MathematicsETH-ZürichZürichSwitzerland
  2. 2.Department of Mathematics, Faculty of EngineeringUniversità di PalermoPalermoItaly
  3. 3.Technikum WinterthurWinterthurSwitzerland
  4. 4.Department of MathematicsWellesley CollegeWellesleyUSA

Bibliographic information