Authors: Antonio Boccuto, Beloslav Riecan, Marta Vrábelová

Kurzweil – Henstock Integral in Riesz Spaces

eBook: US $69 Special Offer (PDF + Printed Copy): US $153
Printed Copy: US $119
Library License: US $276
ISBN: 978-1-60805-405-3 (Print)
ISBN: 978-1-60805-003-1 (Online)
Year of Publication: 2012
DOI: 10.2174/97816080500311090101

Introduction

This Ebook is concerned with both the theory of the Kurzweil-Henstock integral and the basic facts on Riesz spaces. Moreover, even the so-called Šipoš integral, which has several applications in economy, is illustrated. The aim of this Ebook is two-fold. First, it can be understood as an introductory textbook to the Kurzweil-Henstock integral as well as to some algebraic structures which are important from the viewpoint of applications to integration and probability theory. Second, it discusses some possibilities of further developments including recent results and open problems.

Foreword

- Pp. i
Stefan Schwabik
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Preface

- Pp. ii-iii (2)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova
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Contributors

- Pp. iv
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova
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Elementary Introduction to Kurzweil-Henstock Integral

- Pp. 1-24 (24)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Elementary Theory of Riesz Spaces

- Pp. 25-41 (17)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Kurzweil - Henstock Integral with Values in Riesz Spaces

- Pp. 42-51 (10)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Double Integrals

- Pp. 52-61 (10)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Kurzweil - Henstock Integral in Topological Spaces

- Pp. 62-70 (9)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Convergence Theorems

- Pp. 71-83 (13)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Improper Integral

- Pp. 84-110 (27)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Choquet and Sipos Integrals

- Pp. 111-133 (23)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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(SL)-integral

- Pp. 134-165 (32)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Pettis-type Approach

- Pp. 166-177 (12)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Applications in Multivalued Logic

- Pp. 178-186 (9)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Applications in Probability Theory

- Pp. 187-197 (11)
Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

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Integration in Metric Semigroups

- Pp. 198-212 (15)
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References

- Pp. 213-223 (11)
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Index

- Pp. 224-226 (3)
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