Convex sets, metric space of
The family of compact convex sets (cf. Convex set) in a Euclidean space endowed with the Hausdorff metric:
|||B. Grünbaum, "Measures of symmetry for convex sets" , Proc. Symp. Pure Math. , 7 (Convexity) , Amer. Math. Soc. (1963) pp. 233–270|
Metric spaces of convex sets (in particular the metrization by the symmetric difference metric) play a basic role in the foundations of analysis in convex geometry. New important results in convex geometry are given in [a1], [a3]; [a2] gives a general and axiomatic approach.
|[a1]||P.M. Gruber, "Approximation of convex bodies" P.M. Gruber (ed.) J.M. Wills (ed.) , Convexity and its applications , Birkhäuser (1983) pp. 131–162|
|[a2]||H. Hadwiger, "Vorlesungen über Inhalt, Oberfläche und Isoperimetrie" , Springer (1957)|
|[a3]||R. Schneider, "Valuations on convex bodies" P.M. Gruber (ed.) J.M. Wills (ed.) , Convexity and its applications , Birkhäuser (1983) pp. 170–247|
Convex sets, metric space of. V.A. Zalgaller (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Convex_sets,_metric_space_of&oldid=17279