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Factorization calculus and geometric probability /

This unique book develops the classical subjects of geometric probability and integral geometry.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ambartzumian, R. V.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, 1990.
Colección:Encyclopedia of mathematics and its applications ; v. 33.
Temas:
Acceso en línea:Texto completo

MARC

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100 1 |a Ambartzumian, R. V. 
245 1 0 |a Factorization calculus and geometric probability /  |c R.V. Ambartzumian. 
260 |a Cambridge ;  |a New York :  |b Cambridge University Press,  |c 1990. 
300 |a 1 online resource :  |b illustrations 
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490 1 |a Encyclopedia of mathematics and its applications ;  |v v. 33 
504 |a Includes bibliographical references and index. 
588 0 |a Print version record. 
520 |a This unique book develops the classical subjects of geometric probability and integral geometry. 
505 0 |a Cover -- Half Title -- Title -- Copyright -- CONTENTS -- PREFACE -- 1 Cavalieri principle and other prerequisites -- 1.1 The Cavalieri principle -- 1.2 Lebesgue factorization -- 1.3 Haar factorization -- 1.4 Further remarks on measures -- 1.5 Some topological remarks -- 1.6 Parametrization maps -- 1.7 Metrics and convexity -- 1.8 Versions of Crofton's theorem -- 2 Measures invariant with respect to translations -- 2.1 The space G of directed lines on R2 -- 2.2 The space G of (non-directed) lines in R2 -- 2.3 The space E of oriented planes in R3 -- 2.4 The space E of planes in R3. 
505 8 |a 2.5 The space D of directed lines in R3 -- 2.6 The space D of (non-directed) lines in R3 -- 2.7 Measure-representing product models -- 2.8 Factorization of measures on spaces with slits -- 2.9 Dispensing with slits -- 2.10 Roses of directions and roses of hits -- 2.11 Density and curvature -- 2.12 The roses of T3-invariant measures on E -- 2.13 Spaces of segments and flats -- 2.14 Product spaces with slits -- 2.15 Almost sure T-invariance of random measures -- 2.16 Random measures on G -- 2.17 Random measures on E -- 2.18 Random measures on D. 
505 8 |a 3 Measures invariant with respect to Euclidean motions -- 3.1 The group W2 of rotations of R2 -- 3.2 Rotations of R3 -- 3.3 The Haar measure on W3 -- 3.4 Geodesic lines on a sphere -- 3.5 Bi-invariance of Haar measures on Euclidean groups -- 3.6 The invariant measure on G and G -- 3.7 The form of dg in two other parametrizations of lines -- 3.8 Other parametrizations of geodesic lines on a sphere -- 3.9 The invariant measure on D and D. 
505 8 |a 3.10 Other parametrizations of lines in R3 -- 3.11 The invariant measure in the spaces E and E -- 3.12 Other parametrizations of planes in R3 -- 3.13 The kinematic measure -- 3.14 Position-size factorizations -- 3.15 Position-shape factorizations -- 3.16 Position-size-shape factorizations -- 3.17 On measures in shape spaces -- 3.18 The spherical topology of V -- 4 Haar measures on groups of affine transformations -- 4.1 The group Ag and its subgroups -- 4.2 Affine deformations of R2 -- 4.3 The Haar measure on Ag -- 4.4 The Haar measure on A2. 
505 8 |a 4.5 Triads of points in R2 -- 4.6 Another representation of d(r)V -- 4.7 Quadruples of points in R2 -- 4.8 The modified Sylvester problem: four points in R2 -- 4.9 The group Ag and its subgroups -- 4.10 The group of affine deformations of R3 -- 4.11 Haar measures on Ag and A3 -- 4.12 V 3-invariant measure in the space of tetrahedral shapes -- 4.13 Quintuples of points in R3 -- 4.14 Affine shapes of quintuples in R3 -- 4.15 A general theorem -- 4.16 The elliptical plane as a space of affine shapes -- 5 Combinatorial integral geometry -- 5.1 Radon rings in G and G. 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
650 0 |a Stochastic geometry. 
650 0 |a Geometric probabilities. 
650 0 |a Factorization (Mathematics) 
650 6 |a Géométrie stochastique. 
650 6 |a Probabilités géométriques. 
650 6 |a Factorisation. 
650 7 |a MATHEMATICS  |x Probability & Statistics  |x General.  |2 bisacsh 
650 7 |a Factorization (Mathematics)  |2 fast  |0 (OCoLC)fst00919711 
650 7 |a Geometric probabilities.  |2 fast  |0 (OCoLC)fst00940835 
650 7 |a Stochastic geometry.  |2 fast  |0 (OCoLC)fst01133509 
650 7 |a Probabilités géométriques.  |2 ram 
650 7 |a Factorisation (Mathématiques)  |2 ram 
650 7 |a Géométrie stochastique.  |2 ram 
776 0 8 |i Print version:  |a Ambartzumian, R.V.  |t Factorization calculus and geometric probability.  |d Cambridge ; New York : Cambridge University Press, 1990  |z 0521345359  |w (DLC) 89007314  |w (OCoLC)19589158 
830 0 |a Encyclopedia of mathematics and its applications ;  |v v. 33. 
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