Archiv der Mathematik

, Volume 34, Issue 1, pp 377–384 | Cite as

Continuous translation invariant valuations on the space of compact convex sets

  • P. McMullen


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. D. Aleksandrov, On the theory of mixed volumes of convex bodies, III: The extension of two theorems of Minkowski to general convex bodies (Russian). Mat. Sbornik (N.S.)3, 27–46 (1938).Google Scholar
  2. [2]
    T.Bonnesen and W.Fenchel, Theorie der konvexen Körper. Berlin 1934.Google Scholar
  3. [3]
    H.Busemann, Convex surfaces. New York 1958.Google Scholar
  4. [4]
    W. Fenchel andB. Jessen, Mengenfunktionen und konvexe Körper. Danske Vid. Selskab Mat.-fys. Medd.16, 1–31 (1938).Google Scholar
  5. [5]
    W. J. Firey, A functional characterization of certain mixed volumes. Israel J. Math.24, 274–281 (1976).Google Scholar
  6. [6]
    H. Hadwiger, Translationsinvariante, additive und stetige Eibereichfunktionale. Publ. Math. Debrecen2, 81–94 (1951).Google Scholar
  7. [7]
    H. Hadwiger, Translationsinvariante, additive und schwachstetige Polyederfunktionale. Arch. Math.3, 387–394 (1952).Google Scholar
  8. [8]
    H.Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Berlin-Göttingen-Heidelberg 1957.Google Scholar
  9. [9]
    P. McMullen, Valuations and Euler-type relations on certain classes of convex polytopes. Proc. London Math. Soc. (3)35, 113–135 (1977).Google Scholar
  10. [10]
    H.Minkowski, Allgemeine Lehrsätze über die konvexe Polyeder. Nachr. Ges. Wiss. Göttingen 198–219 (1897).Google Scholar
  11. [11]
    C.-H.Sah, Hilbert's third problem: scissors congruence. San Francisco-London-Melbourne 1979.Google Scholar

Copyright information

© Birkhäuser Verlag 1980

Authors and Affiliations

  • P. McMullen
    • 1
  1. 1.Department of MathematicsUniversity CollegeLondon

Personalised recommendations