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A class of convex bodies
Author:
Ethan D. Bolker
Journal:
Trans. Amer. Math. Soc. 145 (1969), 323-345
MSC:
Primary 52.30
MathSciNet review:
0256265
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Additional Information
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- [1]
- A. D. Alexandrov, A theorem on convex polyhedra, Trudy Mat. Inst. Steklov. Sect. Math. 4 (1933), 87. (Russian)
- [2]
- -, Zur Theorie der gemischten Volumina von Konvexen Körpern, II, Neue Ungleichungen zwischen den gemischten Volumina und ihre Anwendungen, Mat. Sb. 2 (1937), 1205-1238. (Russian)
- [3]
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- W. Blaschke, Kreis und Kugel, 2nd ed., de Gruyter, Berlin, 1956. MR 0077958 (17:1123d)
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- W. Blaschke and K. Reidemeister, Über die Entwicklung der Affingeometrie, Jber Deutsch. Math.-Verein. 31 (1922), 63-82.
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- E. Bolker, Functions resembling quotients of measures, Trans. Amer. Math. Soc. 124 (1966), 292-312. MR 0197671 (33:5834)
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- [9]
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- -, Blaschke sums of convex bodies and mixed bodies, Proc. Colloq. on Convexity, (Copenhagen, 1965), Kobenhavns Univ. Mat. Inst., Copenhagen, 1967, pp. 94-101. MR 0220165 (36:3231)
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-unit balls and conical measures, Proc. Amer. Math. Soc. (to appear).
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- B. Grünbaum, Projection constants, Trans. Amer. Math. Soc. 95 (1960), 451-465. MR 0114110 (22:4937)
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- -, Convex polytopes, Wiley, New York, 1967. MR 0226496 (37:2085)
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- P. R. Halmos, The range of a vector measure, Bull. Amer. Math. Soc. 54 (1948), 416-421. MR 0024963 (9:574h)
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- -, Measure theory, Van Nostrand, Princeton, N. J., 1950. MR 0033869 (11:504d)
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- C. S. Herz, A class of negative definite functions, Proc. Amer. Math. Soc. 14 (1963), 670-676. MR 0158251 (28:1477)
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- -, Concrete representation of abstract (M)-spaces (A characterization of the space of continuous functions), Ann. of Math. (2) 42 (1941), 994-1024. MR 0005778 (3:205g)
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- A. Liapounoff, Sur les fonctions-vecteurs complètement additives, Bull. Acad. Sci. URSS Ser. Math. 4 (1940), 465-478. (Russian) MR 0004080 (2:315e)
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- J. Lindenstrauss, On the extension of operators with a finite-dimensional range, Illinois J. Math. 8 (1964), 488-499. MR 0169062 (29:6317)
- [30]
- -, A short proof of Liapounoff's convexity theorem, J. Math. Mech. 15 (1966), 971-972. MR 0207941 (34:7754)
- [31]
- J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in
spaces and their applications, Studia Math. 29 (1968), 275-326. MR 0231188 (37:6743)
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- A. E. Mayer, Grösste Polygone mit gegebenen Seitenvektoren, Comment. Math. Helv. 10 (1938), 288-301. MR 1509581
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- H. Neumann, Beliebige Konvexe Polytope als Schnitte und Projectionen hoherdimensionaler Würfel, Simplizes und Masspolytope, Math. Z. 65 (1965), 91-103. MR 0078701 (17:1233e)
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- N. W. Rickert, The range of a measure, Bull. Amer. Math. Soc. 73 (1967), 560-563. MR 0209435 (35:333)
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- -, Measures whose range is a ball, Pacific J. Math. 23 (1967), 361-371. MR 0222244 (36:5296)
- [39]
- D. Rutovitz, Some parameters associated with finite-dimensional Banach spaces, J. London Math. Soc. 40 (1965), 241-255. MR 0190708 (32:8120)
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- R. Schneider, Zu einem Problem von Shephard über die Projectionen konvexer Körper, Math. Z. 101 (1967), 71-82. MR 0218976 (36:2059)
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- -, Über eine Integralgleichung in der Theorie der konvexen Körper, Math. Nachr. (to appear). MR 0275286 (43:1043)
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- G. Schwarz, Variations on vector measures, Pacific J. Math. 23 (1967), 373-375. MR 0220894 (36:3946)
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- Z. Semadeni, Generalizations of Bohr's theorem on Fourier series with independent characters, Studia Math. 23 (1963), 159-179. MR 0169001 (29:6256)
- [44]
- G. C. Shephard, Decomposable convex polyhedra, Mathematika 10 (1963), 89-95. MR 0172176 (30:2398)
- [45]
- -, Approximation problems for convex polyhedra, Mathematika 11 (1964), 9-18. MR 0172177 (30:2399)
- [46]
- -, Polytopes with centrally symmetric faces, Canad. J. Math. 19 (1967), 1206-1213. MR 0221381 (36:4433)
- [47]
- G. Choquet, Mesures coniques, affines et cylindriques, Instituto Nazionale di Alta Matematica, Symposia Matematica, Vol. II, Gubbio, 1968. MR 0261306 (41:5921)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1969-0256265-X
PII:
S 0002-9947(1969)0256265-X
Article copyright:
© Copyright 1969 American Mathematical Society
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