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:
Stochastic geometry.
Geometric probabilities.
Factorization (Mathematics)
Géométrie stochastique.
Probabilités géométriques.
Factorisation.
MATHEMATICS > Probability & Statistics > General.
Factorisation (Mathématiques)
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.

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