Authors: Antonio Boccuto, Xenofon Dimitriou

Convergence Theorems For Lattice Group-Valued Measures

eBook: US $69 Special Offer (PDF + Printed Copy): US $209
Printed Copy: US $175
Library License: US $276
ISBN: 978-1-68108-010-9 (Print)
ISBN: 978-1-68108-009-3 (Online)
Year of Publication: 2015

Introduction

Convergence Theorems for Lattice Group-valued Measures explains limit and boundedness theorems for measures taking values in abstract structures. The book begins with a historical survey about these topics since the beginning of the last century, moving on to basic notions and preliminaries on filters/ideals, lattice groups, measures and tools which are featured in the rest of this text. Readers will also find a survey on recent classical results about limit, boundedness and extension theorems for lattice group-valued measures followed by information about recent developments on these kinds of theorems and several results in the setting of filter/ideal convergence. In addition, each chapter has a general description of the topics and an appendix on random variables, concepts and lattices is also provided. Thus readers will benefit from this book through an easy-to-read historical survey about all the problems on convergence and boundedness theorems, and the techniques and tools which are used to prove the main results. The book serves as a primer for undergraduate, postgraduate and Ph. D. students on mathematical lattice and topological groups and filters, and a treatise for expert researchers who aim to extend their knowledge base.

Foreword

- Pp. i-ii (2)
Christos P. Kitsos
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Preface

- Pp. iii-iv (2)
Antonio Boccuto and Xenofon Dimitriou
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About the Authors

- Pp. v
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Historical Survey

- Pp. 3-139 (137)
Antonio Boccuto and Xenofon Dimitriou

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Basic Concepts and Results

- Pp. 140-262 (123)
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Classical Limit Theorems in Lattice Groups

- Pp. 263-358 (96)
Antonio Boccuto and Xenofon Dimitriou

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Filter/Ideal Limit Theorems

- Pp. 359-493 (135)
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General Discussion

- Pp. 494-498 (5)
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Appendix

- Pp. 499-508 (10)
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References

- Pp. 509-532 (24)
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Index

- Pp. 533-537 (5)
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