Integral geometry in homogeneous spaces
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- by John E. Brothers
- Trans. Amer. Math. Soc. 124 (1966), 480-517
- DOI: https://doi.org/10.1090/S0002-9947-1966-0202099-9
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References
- A. S. Besicovitch, On existence of subsets of finite measure of sets of infinite measure, Nederl. Akad. Wetensch. Proc. Ser. A. 55 = Indagationes Math. 14 (1952), 339–344. MR 0048540
- A. S. Besicovitch and P. A. P. Moran, The measure of product and cylinder sets, J. London Math. Soc. 20 (1945), 110–120. MR 16448, DOI 10.1112/jlms/s1-20.2.110 J. E. Brothers, Integral geometry in homogeneous spaces, Ph. D. thesis, Brown University, Providence, R. I., 1964.
- Shiing-shen Chern, On integral geometry in Klein spaces, Ann. of Math. (2) 43 (1942), 178–189. MR 6075, DOI 10.2307/1968888
- Claude Chevalley, Theory of Lie groups. I, Princeton University Press, Princeton, N. J., 1946 1957. MR 0082628 G. DeRham, Variétés différentiables, Actualités Sci. Indust. No. 1222, Hermann, Paris, 1955.
- Herbert Federer, The $(\varphi ,k)$ rectifiable subsets of $n$-space, Trans. Amer. Math. Soc. 62 (1947), 114–192. MR 22594, DOI 10.1090/S0002-9947-1947-0022594-3
- Herbert Federer, Dimension and measure, Trans. Amer. Math. Soc. 62 (1947), 536–547. MR 23325, DOI 10.1090/S0002-9947-1947-0023325-3
- Herbert Federer, Some integralgeometric theorems, Trans. Amer. Math. Soc. 77 (1954), 238–261. MR 63686, DOI 10.1090/S0002-9947-1954-0063686-6 —, An analytic characterization of distributions whose partial derivatives are representable by measures, Bull. Amer. Math. Soc. 60 (1954), 339, Abstract 407.
- Herbert Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959), 418–491. MR 110078, DOI 10.1090/S0002-9947-1959-0110078-1
- Herbert Federer, Some theorems on integral currents, Trans. Amer. Math. Soc. 117 (1965), 43–67. MR 168727, DOI 10.1090/S0002-9947-1965-0168727-0
- Herbert Federer and Wendell H. Fleming, Normal and integral currents, Ann. of Math. (2) 72 (1960), 458–520. MR 123260, DOI 10.2307/1970227
- Gerald Freilich, On the measure of Cartesian product sets, Trans. Amer. Math. Soc. 69 (1950), 232–275. MR 37893, DOI 10.1090/S0002-9947-1950-0037893-9
- Jun-ichi Hano, On Kaehlerian homogeneous spaces of unimodular Lie groups, Amer. J. Math. 79 (1957), 885–900. MR 95979, DOI 10.2307/2372440
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
- Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1963. MR 0152974
- J.-L. Koszul, Exposés sur les espaces homogènes symétriques, Sociedade de Matemática de São Paulo, São Paulo, 1959 (French). Publicação da Sociedade de Matemática de São Paulo. MR 0132804
- Klaus Krickeberg, Distributionen, Funktionen beschränkter Variation und Lebesguescher Inhalt nichtparametrischer Flächen, Ann. Mat. Pura Appl. (4) 44 (1957), 92, 105–133 (German). MR 95922, DOI 10.1007/BF02415194
- Minoru Kurita, An extension of Poincaré formula in integral geometry, Nagoya Math. J. 2 (1951), 55–61. MR 40687
- Lynn H. Loomis, The intrinsic measure theory of Riemannian and Euclidean metric spaces, Ann. of Math. (2) 45 (1944), 367–374. MR 9976, DOI 10.2307/1969274
- Tadashi Nagano, Homogeneous sphere bundles and the isotropic Riemann manifolds, Nagoya Math. J. 15 (1959), 29–55. MR 108810 S. Saks, Theory of the integral, Monografie Matematyczne No. 7, Warsaw, 1937.
- Arthur Sard, The equivalence of $n$-measure and Lebesgue measure in $E_n$, Bull. Amer. Math. Soc. 49 (1943), 758–759. MR 8837, DOI 10.1090/S0002-9904-1943-08025-1
- I. I. Pjateckiĭ-Šapiro, On a problem proposed by E. Cartan, Dokl. Akad. Nauk SSSR 124 (1959), 272–273 (Russian). MR 0101922
- Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. MR 0039258 A. Weil, L’intégration dans les groups topologiques et ses applications, Actualités Sci. Indust. No. 869, Hermann, Paris, 1938.
- Hassler Whitney, Geometric integration theory, Princeton University Press, Princeton, N. J., 1957. MR 0087148
Bibliographic Information
- © Copyright 1966 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 124 (1966), 480-517
- MSC: Primary 53.90; Secondary 53.66
- DOI: https://doi.org/10.1090/S0002-9947-1966-0202099-9
- MathSciNet review: 0202099