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| Santalo L., Kac M. — Integral geometry and geometric probability |
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| Предметный указатель |
Abel's integral equation 288 289
Adjoint representation 150 159 160
Admissible domains 138
Affine groups 179—182
Affine groups, homogeneous 181
Affine groups, special 180 187
Affine groups, special homogeneous 183
Affine groups, special nonhomogeneous 182 187
Affinity 179
Agglomerations of convex sets 279
Aggregates of ellipsoids 291
Aggregates of points 102
Aggregates of spheres 290
Ahlfors, L. 343 344
Ailan, G. 276(2)
Algebraic manifolds 343
Alikoski, A.A. 64
Allendoerfer, C.B. 302 304(4) 322
Almost bundle 280
Ambarcumjan inequality 37 231
Ambarcumjan, R.V. 20 34 37 102 231 250
Anderssen, R.S. 290(321 322) 291
Angle formula 238
Angle in n.e. geometry 302
Annihilator 146
Area of convex set 3 60
Armitage, P. 101
Arnold, V.I. 40
Asymmetry 38
Averages for curves 111
Averages for polygons 55
Averages for polyhedrons 296
Avez, A. 40
Axial vectors 360
Azorin, F. 294(15 16)
Bach, G. 286
Balanzat, M. 98(17 18)
Bambah, R.P. 10
Banchoff, T.F. 38 252
Barbier, E. 111
Bate, A.E. 62(22)
Baticle, M. 24
Bender, E.A. 138
Benson, D.C. 124 232
Benson, R.V. 1
Berger, M. 351
Bernal, J.D. 26
Berwald, L. 197
Bezout theorem 343
Bieberbach, L. 41 (30a)
Birkhoff, G.D. 40
Bishop, R.L. 143
Blaschke's fundamental formula 113—116
Blaschke, W. 1 31(50) 36 40(40) 48 59 64 113 114 118 121 125 197 200(30) 201 211 238(35) 260 281(51) 311 312 340(47) 341(47) 347 351(39)
Blichfeldt's theorem 137
Blichfeldt's theorem, generalized 176
Blichfeldt, H.F. 137 175 176
Bodzioni, J. 211(54—56) 290
Bohm, J. 311
Bokowski, J. 138
Bol, G. 120
Boltjanski, V.G. 1
Bonnesen's inequality 120
Bonnesen, T. 1 3(63) 4(63) 8(63) 120 124 125 126 215(63) 217 231(63) 249(63) 267(63) 324(62)
Borel, E. 108
Borovikov, V.A. 348
Bottema, O. 121
Bourbaki, N. 178
Breadth 6
Breadth of strip 68
Briarty, L.G. 282(70)
Bronowski, J. 276
Brothers, J.E. 277
Buffon's Needle Problem 71 107 135
Buffon's needle problem with broken line 77
Buffon's needle problem, generalized 77 250 281
Busemann, H. 209 215(74) 300
Calugareanu, G. 252
Caregradskii, I.P. 103(80) see
Carleman, T. 48 238(81)
Carlson, J.A. 343
Carnal, H. 23 147
Cartan's Lemma 357
Cartan, E. 145(85) 151 152 153 154 180 211 331 339(89) 342(86) 353
Cartan, H. 12 353 359
Cartesian space  179
Cassels, J.W.S. 10 190
Cauchy's formula 217
Cauchy, A. 218
Chain rule 177
Chakerian, G.D. 125 126 138 232 255(96 97) 351(95)
Chebotarev, N.G. 177
Chen, Chang-shing 276 277
Chern, S.S. 113(111) 171 242 254 260 262 276 302 343 344
Chevalley, C. 353
Clark, J.M. 48
Class  3
Class of curve 344
Close packing of segments 126
Closed differential forms 359
Closed geodesics 351
Closed subgroups 165
Clumps of convex sets 101
Clusters 102 213
Coefficient of inefficiency 67
Coleman, R. 23 24 63
Commutative groups 156
Compact groups 159
Complete set of inequalities 10
Completely integrable 146
Complex analytic mappings 343
Complex spaces 338
Concurrent cross sections 209
Congruences, of geodesics 334 335
Congruences, of lines 211 254
Conjugate points 300
Constant breadth 8
Convex billiard 40
Convex body 215
Convex body in elliptic space 322
Convex body of various shapes 229
Convex curves 1
Convex hull 32
Convex hull of n random points 22
Convex ring 350
Convex sets 1 215
Convex sets at random in  283
Convex sets in  215
Convex sets, contained in another 94 95
Convex sets, intersecting another 93 94
Convex surface 215
Cooke, P.J. 99
Corte, H. 67
Cotangent space 82 144
Courant, R. 288(125)
Covectors in 354
Cover, T. 328 329
Coverage problems on circle 25
Coverage problems on line 24 25
Coverage problems on plane 98
Coverage problems on sphere 325—327
Coxeter, H.S.M. 19 113 128 311
Crain, I.K. 20
Crofton's formulas in  237—239
Crofton's formulas in n.e. spaces 316
Crofton's formulas in plane 47 51
Crofton, M.W. 13 21 47 51 58
Crystallographic groups 128
cube 229
Cubic particles 293
| Curvature of Chern — Lashof 254
Curvature of space 300
Cylinders in 280
Cylinders in 270
Cylinders, intersecting ball 279
Cylinders, intersecting convex sets 273
Czuber, E. 16 21
Daley, D.J. 67
Darboux's theorem 362
Darling, D.A. 60
Davidson, R. 58 66 67
De Hoff, R.T. 289 290
De Rahm, G. 343
de Vries, H.L. 59 (145a)
Deltheil, R. 13 51(143) 63(143) 198(144) 212 233(144)
Density for cylinders 270 280
Density for horocycles 314
Density for hyperplanes 184 185
Density for linear spaces in 199
Density for linear spaces in  340
Density for lines 27 28
Density for m-tuples of linear spaces 186 193
Density for normal chains 341
Density for pairs of linear spaces 205
Density for pairs of lines 49 194
Density for pairs of points 45
Density for parallel hyperplanes 188
Density for parallel subspaces 190
Density for parallelograms 194
Density for planes and lines in 210
Density for points 13 173
Density for points and lines 195
Density for r-planes 183 187 204 305
Density for r-planes about a q-plane 202
Density for strips 68
Density for triples of points 16
Density function for area 18
Density function for orthogonal projection 218
Density function for perimeter 17
Density function for radii of circumdisk 19
Diameter 6
Difference set 125
Differential forms 82 353
Differential forms over manifolds 361
Differential forms over the group of motions 82
Differential forms, closed 359
Differential forms, decomposable 356
Differential forms, exact 359
Differential of a mapping 148
Differential of a mapping, dual 148
Direct product of groups 161
Distances in n-ball 212
Distances in the space of graphs 42
Distances of two curves 38
Distances, non-euclidean 301
Distribution of areas of triangles 19
Distribution of distances in n-ball 212
Distribution of lengths of chords 48
Distribution of particles 282
Distribution of radii of circumdisks 19
Distribution of sizes of particles 291
Division of a body by random planes 294
Division of a convex set by random lines 54
Division of plane by random lines 51—58
dodecahedron 229
Dodson, C.T.J. 67
Domain 128
Domb, C. 213
Drinfel'd, G.I. 177
Dual formulas 303
Dual formulas in elliptic space 318
Duffin, R., J. 290 291
Dufour, S.W. 104
Dvoretzky, A. 11 25
Eberhardt, L.L. 24
Effective Lie transformation group 173
Efron, B. 23 328 329
Eggleston, H.G. 1 189
Eisenhart, L.P. 247(165) 254(165) 308(165)
Elias, H. 226(166) 282 286 290(166)
Ellipsoid 249 291
Elliptic n.e. space 300
Envelope 2
Equations of Rodrigues 264 302 320
Euclidean space 196
Euler characteristic 113
Euler — Poincare characteristic 223
Eulerian graph 42
Exact differential form 359
Exterior derivative 144 358
Exterior differential 358
Exterior product 353—357
External cover 32
Fairthone, D. 49
Fary, I. 35 254 255
Fast, H. 31(171)
Favard length 31
Favard measure 248
Favard, J. 31 248
Fazekas de St. Groth, S. 327
Federer, H. 248 260 276 277 303
Fejes Toth, L. 127(181) 137(179)
Feller, W. 41
Fenchel, W. 1 3(63) 4(63) 8(63) 126 215(63) 217 231(63) 249(63) 254 267(63)
Fields of convex sets 100 278
Fields of cylinders 278
Figiel, T. 218(188)
Filipescu, D. 98 280(190 191)
Fillmore, J.P. 315
Firey, W.J. 10(192) 215(195) 231 249 333
Fisher, L.D. 23
Fisher, R.A. 24 294(199)
Fixed frame 87
Flaherty, F.J. 276
Flanders, H. 12 125 147 353
Flattened convex body 227
Fleming, W.H. 12 362
Foliated spaces 330
Foliation 331
Forms linearly independent 357
Forms of degree r 356
Fratila, E. 72(205)
Fujiwara, M. 120
Fukunaga, K. 294(206a)
Functions over straight lines 60
Fundamental kinematic formula 113—115 262—266
Fundamental kinematic formula for convex sets 267
Fundamental kinematic formula for cylinders 270 271
Fundamental kinematic formula for strips 118
Fundamental kinematic formula in n.e. spaces 320 321
Fundamental quadric 299
Fundamental region 128
Funk, P. 347
Furstenberg, H. 249
Gaeta, F. 171(211)
Gamma distribution 18
Gani, J. 26
Garwood, F. 24 67(213)
Gaspar, E. 75(216)
Gauss — Bonnet formula 302
Gaussian distribution 291
Geciauskas, E.P. 48 63 103(219) 108(217)
Geffroy, J. 23
Gelfand's integral geometry 345
Gelfand, I.M. 345 346 347 348
General affine group 180 182
General linear group GL(n) 149
Geodesic curvature 303
Geodesic segments 338
Geodesics 331
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