Convexity

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CUP Archive, 1958 - Mathematics - 136 pages
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This account of convexity includes the basic properties of convex sets in Euclidean space and their applications, the theory of convex functions and an outline of the results of transformations and combinations of convex sets. It will be useful for those concerned with the many applications of convexity in economics, the theory of games, the theory of functions, topology, geometry and the theory of numbers.
 

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Contents

Convex polytopes
29
The relation of Hellys theorem to Caratheodorys
39
general properties
45
Differential conditions for convexity
51
approximations to convex sets
59
Approximations by convex polytopes and regular
67
Sets and numbers associated with a convex set
76
Mixed volumes
82
Surface area
88
the Minkowski
96
some special problems
103
Relations between the inradius circ urn radius
111
sets of constant width
122
Minimal universal covers
131
References
139
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