BN.com Gift Guide

Theory of Random Sets / Edition 1

Hardcover (Print)
Buy New
Buy New from BN.com
$111.20
Used and New from Other Sellers
Used and New from Other Sellers
from $99.40
Usually ships in 1-2 business days
(Save 28%)
Other sellers (Hardcover)
  • All (8) from $99.40   
  • New (5) from $99.40   
  • Used (3) from $102.92   

Overview

"Stochastic geometry is a relatively new branch of mathematics. Although its predecessors such as geometric probability date back to the 18th century, the formal concept of a random set was developed in the beginning of the 1970s. Theory of Random Sets presents a state-of-the-art treatment of the modern theory, but it does not neglect to recall and build on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference of the 1990s. The book is entirely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight." The book will be an invaluable reference for probabilists, mathematicians in convex and integral geometry, set-valued analysis, capacity and potential theory, mathematical statisticians in spatial statistics and image analysis, specialists in mathematical economics, and electronic and electrical engineers interested in image analysis.
Read More Show Less

Editorial Reviews

From the Publisher

From the reviews:

"Together with the foundations of the modern probability theory Kolmogorov introduced the concept of a random set. … The book is written in a theorem-proof style, where the proofs are quite detailed and clearly presented. … to enable easier reading, the author provides visual illustrations where necessary. … the author provides a vast bibliography on the subject, which is completely searchable on author’s website. The book should be read and even more studied by any researcher or a student considering research in this field." (Ita Cirovic Donev, MathDL, January, 2006)

"This book is part of the Springer-Verlag series ‘Probability and its applications’. … The most remarkable aspect of the book is the reader-friendly structure and the style in which it has been written. There are masses of examples either worked out in the book or left for the reader. A number of facts are equipped with graphical illustrations. This book has a good index and index of notations, and a very detailed bibliography … . It will be an essential part of every mathematical library." (V. K. Oganyan, Mathematical Reviews, Issue 2006 b)

"The book under review develops … an approach in a self-contained and systematic manner. Full proofs are given, and many steps are illustrated by graphs and drawings. The interdisciplinary nature of the theory of random sets within mathematics is well shown. … The book will be an invaluable reference for probabilists, mathematicians, statisticians and electronic and electrical engineers in the fields of image analysis. … The book is highly recommended both for personal use and for libraries." (Janos Galambos, Zentralblatt MATH, Vol. 1109 (11), 2007)

"Random sets play an important role in many applications of mathematics … . This book is an important contribution to the mathematical theory and will surely serve as a valuable textbook for students as well as researchers. It presents a self-contained survey of all the significant results … . A number of open problems are presented and each chapter concludes with a list of bibliographical notes." (EMS Newsletter, September, 2007)

Read More Show Less

Product Details

  • ISBN-13: 9781852338923
  • Publisher: Springer London
  • Publication date: 4/14/2005
  • Series: Probability and Its Applications Series
  • Edition description: 2005
  • Edition number: 1
  • Pages: 488
  • Product dimensions: 1.13 (w) x 9.21 (h) x 6.14 (d)

Meet the Author

Ilya Molchanov is Professor of Probability Theory in the Department of Mathematical Statistics and Actuarial Science at the University of Berne, Switzerland.

Read More Show Less

Table of Contents

1 Random closed sets and capacity functionals 1
2 Expectations of random sets 145
3 Minkowski addition 195
4 Unions of random sets 241
5 Random sets and random functions 303
App. A Topological spaces and linear spaces 387
App. B Space of closed sets 398
App. C Compact sets and the Hausdorff metric 402
App. D Multifunctions and semicontinuity 409
App. E Measures, probabilities and capacities 412
App. F Convex sets 421
App. G Semigroups and harmonic analysis 425
App. H Regular variation 428
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)