Topics in Banach space integration / Stefan Schwabik, Ye Guoju.

Format:

Book

Author/Creator:

Schwabik, Štefan, 1941-

Contributor:

Ye, Guoju.

Series:

Series in real analysis ; v. 10.

Series in real analysis ; v. 10

Language:

English

Subjects (All):

Banach spaces.

Integrals.

Physical Description:

1 online resource (313 p.)

Edition:

1st ed.

Place of Publication:

New Jersey : World Scientific, c2005.

Language Note:

English

Summary:

The relatively new concepts of the Henstock-Kurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The Henstock-Kurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.

Contents:

Preface; Notation; Contents; 1. Bochner Integral; 2. Dunford and Pettis Integrals; 3. McShane and Henstock-Kurzweil Integrals; 4. More on the McShane Integral; 5. Comparison of the Bochner and McShane Integrals; 6. Comparison of the Pettis and McShane Integrals; 7. Primitive of the McShane and Henstock-Kurzweil Integrals; 8. Generalizations of Some Integrals; Appendix A Classical Banach Spaces; Appendix B Series in Banach Spaces; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 291-296) and index.

ISBN:

9786611899233

9781281899231

1281899232

9789812703286

9812703284

OCLC:

476064684