A problem of geometry in

Authors:
M. Katchalski and A. Liu

Journal:
Proc. Amer. Math. Soc. **75** (1979), 284-288

MSC:
Primary 52A35

DOI:
https://doi.org/10.1090/S0002-9939-1979-0532152-6

MathSciNet review:
532152

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite family of at least convex sets in the *n*-dimensional Euclidean space . Helly's theorem asserts that if all the -subfamilies of have nonempty intersection, then also has nonempty intersection. The main result in this paper is that if almost all of the -subfamilies of have nonempty intersection, then has a subfamily with nonempty intersection containing almost all of the sets in .

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DOI:
https://doi.org/10.1090/S0002-9939-1979-0532152-6

Article copyright:
© Copyright 1979
American Mathematical Society