Factorization calculus and geometric probability /
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| Author / Creator: | Ambartzumian, R. V. |
|---|---|
| Imprint: | Cambridge ; New York : Cambridge University Press, 1990. |
| Description: | 1 online resource : illustrations |
| Language: | English |
| Series: | Encyclopedia of mathematics and its applications ; v. 33 Encyclopedia of mathematics and its applications ; v. 33. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11200782 |
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| 100 | 1 | |a Ambartzumian, R. V. |0 http://id.loc.gov/authorities/names/n81094224 | |
| 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 | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 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 <U+0044> of directed lines in R3 -- 2.6 The space <U+0044> 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 <U+0044>. | |
| 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 <U+0044> and <U+0044>. | |
| 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 <U+0056> -- 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. | |
| 650 | 0 | |a Stochastic geometry. | |
| 650 | 0 | |a Geometric probabilities. |0 http://id.loc.gov/authorities/subjects/sh85054125 | |
| 650 | 0 | |a Factorization (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85046844 | |
| 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 | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 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. |0 http://id.loc.gov/authorities/names/n42010632 | |
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| 928 | |t Library of Congress classification |a QA273.5 |l Online |c UC-FullText |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=569270 |z eBooks on EBSCOhost |g ebooks |i 12393037 | ||