The Bartle-Dunford-Schwartz Integral

Treats in detail the vectorial Radon integration Explores an interplay between, on the one side, linear operators, transfering real (complex) functions onto elements of locally convex Hausdorff spaces, and vector-valued measures, on the other Includes supplementary material: sn.pub/extras

Texte du rabat

This volume is a thorough and comprehensive treatise on vector measures. The functions to be integrated can be either [0,infinity]- or real- or complex-valued and the vector measure can take its values in arbitrary locally convex Hausdorff spaces. Moreover, the domain of the vector measure does not have to be a sigma-algebra: it can also be a delta-ring. The book contains not only a large amount of new material but also corrects various errors in well-known results available in the literature. It will appeal to a wide audience of mathematical analysts. TOC:Preface.- 1. Preliminaries.- 2. Basic Properties of the Bartle-Dunford-Schwartz Integral.- 3. Lp-Spaces.- 4. Integration with Respect to LcHs-valued Measures.- 5. Applications to Integration in Locally Compact Hausdorff Spaces I.- 6. Applications to Integration in Locally Compact Hausdorff Spaces II.- 7. Complements to the Thomas Theory of Vectorial Radon Integration.- References.- List of symbols.- Index.

Résumé
This volume is a thorough and comprehensive treatise on vector measures, treating the vectorial Radon integration in detail. It explores an interplay between, on the one side, linear operators, transferring real (complex) functions onto elements of locally convex Hausdorff spaces, and vector-valued measures, on the other. The book contains not only a large amount of new material but also corrects various errors in well-known results available in the literature.

Contenu
Preliminaries.- Basic Properties of the Bartle-Dunford-Schwartz Integral.- Lp-spaces, 1 ? p ? ?.- Integration With Respect to lcHs-valued Measures.- Applications to Integration in Locally Compact Hausdorff Spaces Part I.- Applications to Integration in Locally Compact Hausdorff Spaces Part II.- Complements to the Thomas Theory of Vectorial Radon Integration.