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Ein Approximationssatz für konvexe Körper. (German) Zbl 0251.52007


MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
26A51 Convexity of real functions in one variable, generalizations
44A35 Convolution as an integral transform
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
28A10 Real- or complex-valued set functions
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References:

[1] ALEKSANDROV, A. D.: Zur Theorie der gemischten Volumina von konvexen Körpern I. (Russisch) Mat. Sbornik, n. Ser. 2, 947-972 (1937). · Zbl 0017.42603
[2] ALEKSANDROV, A. D.: Almost everywhere existence of second differentials of convex functions. (Russisch), Leningrad. gosudarst. ped. Inst. A. I. Gercen, u?enye Zapiski 6, 3-35 (1939).
[3] BERG, C.: Corps convexes et potentiels sphêriques. Mat.-fys. Medd., Danske Vid. Selsk. 37, 6 (1969). · Zbl 0181.38303
[4] BONNESEN, T., FENCHEL, W.: Theorie der konvexen Körper, Berlin: Springer 1934. · Zbl 0008.07708
[5] FENCHEL, W., JESSEN, B.: Mengenfunktionen und konvexe Körper. Mat.-fys. Medd., Danske Vid. Selsk. 16, 3 (1938). · Zbl 0018.42401
[6] FIREY, W. J.: Christoffel’s problem for general convex bodies. Mathematika, London 15, 7-21 (1968). · Zbl 0162.54303
[7] HAMMER, P. C.: Approximation of convex surfaces by algebraic surfaces. Mathematika, London 10, 64-71 (1963). · Zbl 0122.41004
[8] HEWITT, E., STROMBERG, K.: Real and abstract analysis, 2. Aufl. Berlin-Heidelberg-New York: Springer 1969. · Zbl 0225.26001
[9] NATANSON, I. P.: Theorie der Funktionen einer reellen Veränderlichen, 2. Aufl. Berlin: Akademie-Verl. 1961.
[10] POGORELOV, A. V.: On a regular solution of the n-dimensional Minkowski problem. Soviet Math., Doklady 12, 1192-1196 (1971) (Transl. of Doklady Akad. Nauk SSSR 199, 785-788 (1971)). · Zbl 0236.53057
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