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Tuesday, May 19, 2020 | History

8 edition of Integral geometry and geometric probability found in the catalog.

Integral geometry and geometric probability

by Luis A. SantalГі

  • 130 Want to read
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Published by Cambridge University Press in Cambridge, UK, New York .
Written in English

    Subjects:
  • Geometric probabilities,
  • Integral geometry

  • Edition Notes

    Includes bibliographical references (p. 363-394) and indexes.

    StatementLuis A. Santaló ; with a foreword by Mark Kac.
    SeriesCambridge mathematical library
    Classifications
    LC ClassificationsQA273.5 .S26 2004
    The Physical Object
    Paginationxvii, 404 p. :
    Number of Pages404
    ID Numbers
    Open LibraryOL3439440M
    ISBN 100521523443
    LC Control Number2005298787
    OCLC/WorldCa52055341

    Integral geometry sprang from the principle that the mathematically natural probability models are those that are invariant under certain transformation groups. This topic emphasises systematic development of formulas for calculating expected values associated with the geometric objects derived from random points, and can in part be viewed as a. [ale04a] S. Alesker, "Hard Lefschetz theorem for valuations and related questions of integral geometry," in Geometric Aspects of Functional Analysis, New York: Springer-Verlag, , vol. , pp. Cited by:

    This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to. Geometric probability is a tool to deal with the problem of infinite outcomes by measuring the number of outcomes geometrically, in terms of length, area, or volume. In basic probability, we usually encounter problems that are "discrete" (e.g. the outcome of a dice roll; see probability by outcomes for more). However, some of the most interesting problems involve "continuous" variables (e.g.

    Full Description:" Analysis, geometry and probability gives motivation to analyze information and is also useful when criticizing plots; or it is a well-written section if the character is properly designed, if the narrative sounds innocent, etc. If you ever have the opportunity to discuss the book with others, you will be able to clearly tell their views, as you have taken the time to really. Introduction to Geometric Probability by Daniel A. Klain and Gian-Carlo Rota. This is a modern introduction to geometric probability, also known as integral geometry. The subject is presented at an elementary level, requiring little more than first year graduate mathematics.


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Integral geometry and geometric probability by Luis A. SantalГі Download PDF EPUB FB2

Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology).

The book is a systematic exposition of the theory and Cited by: Additional Physical Format: Online version: Santaló, Luis A. (Luis Antonio), Integral geometry and geometric probability.

Reading, Mass.: Addison-Wesley. Integral Geometry and Geometric Probability (Cambridge Mathematical Library) - Kindle edition by Santaló, Luis A., Kac, Integral geometry and geometric probability book. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Integral Geometry and Geometric Probability (Cambridge Mathematical Library).4/5(1).

Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments, however, have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology).Cited by: Integral geometry and geometric probability.

[Luis Antonio Santaló; Mark Kac] The book should serve as an excellent text for a graduate course on integral ' Bulletin of the American Mathematical Society. # Integral geometry\/span>\n \u00A0\u00A0\u00A0\n schema.

where is a set of points in the parameter space of the Lie group and is an integral invariant of the group, defined by equation (1), or the density measure.

The integral in (2) is also called an elementary measure of the set of manifolds. A specific choice of this measure sets up a complete correspondence with the fundamental problem in the study of geometric probabilities.

Integral Geometry, known in applied circles as Geometric Probability, is somewhat of a mathematical antique (and therefore it is a favorite of mine!) From it developed many modern topics: geometric measure theory, stereometry, tomography, characteristic classes 1 Integral geometry examples: Buffon’s needle problem.

Firery’s dice problemFile Size: KB. It develops, in a measure-theoretic setting, the integral geometry for the motion and the translation group, as needed for the investigation of these models under the usual invariance assumptions.

A characteristic of the book is the interplay between stochastic and geometric arguments, leading to. What is the probability that a random straight line in What is Integral Geometry. The title of this book, Geometric Tomography, is designed to cover the area of mathematics dealing with the retrieval of information about a geometric object from data about its sections.

Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology).5/5(1).

Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology).

The book is a systematic exposition of the theory and a compilation of the main results in the field. Here is the first modern introduction to geometric probability, also known as integral geometry, presented at an elementary level, requiring little more than first-year graduate mathematics.

Klein and Rota present the theory of intrinsic volumes due to Hadwiger, McMullen, Santaló and others, along with a complete and elementary proof of Hadwiger's characterization theorem of invariant. The book is a systematic exposition of the theory and a compilation of the main results in the field.

The volume can be used to complement courses on differential geometry, Lie groups or probability or differential geometry. It is ideal both as a reference and for those wishing to enter the field. Integral Geometry and Geometric Probability. Learn how to find geometric probabilities in this free math video tutorial by Mario's Math Tutoring.

Probability Formula Introductory Example Example 1 Find the Probability for. Santaló, L. A., Integral Geometry and Geometric Probability, (Encyclopedia of Mathematics and Its Applications) 1. London‐Amsterdam‐Don Mills‐Sydney‐Tokyo, Addison‐Wesley Publishing Company XVII, S., $ Cited by: 2.

Buy Integral Geometry and Geometric Probability (Cambridge Mathematical Library) 2 by Luis Santaló (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on. Integral geometry originated with problems on geometrical probability and convex bodies.

Its later developments, however, have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology).

Open Library is an open, editable library catalog, building towards a web page for every book ever published. Integral geometry and geometric probability by Luis A. Santaló; 3 editions; First published in ; Subjects: Geometric probabilities, Integral geometry.

To calculate the probability that a given number of trials take place until the first success occurs, use the following formula: P(X = x) = (1 – p) x – 1 p for x = 1, 2, 3, Here, x can be any whole number (integer); there is no maximum value for x. X is a geometric random variable, x is the number of trials required until the first success occurs, and p is the probability of success.

Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations.5/5(1).

Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets.There are two strands of integral geometry.

One involves the study of measures or Buffon’s needle problem about the probability that a line segment of given length placed randomly on the plane would intersect a horizontal line of the form y I would highly recommend Helgason’s upcoming book Integral Geometry and Radon Transforms [  As an introduction to the subjects of integral geometry and geometric probability, Langevin’s book should be read alongside the classic text by Santaló.

Santaló’s text is more concerned with probabilistic questions about geometric figures in the plane, though the latter chapters deal somewhat cursorily with topics expounded in more detail.