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On the separating number of a finite family of charges

✍ Scribed by K. P. S. Bhaskara Rao; M. Bhaskara Rao

Publisher
John Wiley and Sons
Year
1981
Tongue
English
Weight
160 KB
Volume
101
Category
Article
ISSN
0025-584X

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✦ Synopsis

A charge is a finitely additive, real valued, non-negative set function defined on a field d of subsets of a set X vanishing a t the empty set. A natural number n is said to be the separating number of a finite family pi, p 2 , . . . , pK of charges on 8 if there exists sets PI, F 2 , . . . , Fa in d satisfying the following properties.

(iii) Given any distinct i and j in (1, 2, . . . , K } , there exists a p in ( 1 , 2, . . . , n} such that pi(Fp) + p j ( F p ) . (iv) If {E,} is any family of sets i n 8 satisfying (i), (ii) and (iii), then the cardinality of the family {E,} is s n . VISHIK, KOBRINSKII and ROSENTAL [ 5 , p. 1481 proved the following result.

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