RECURRENCE IN ERGODIC THEORY AND COMBINATORIAL NUMBER THEORY
RECURRENCE IN ERGODIC THEORY AND COMBINATORIAL NUMBER THEORY
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DOI：
10.1112/blms/14.5.458
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发表时间：
1982-09
影响因子：
0.9
通讯作者：
L. Vaserstein
中科院分区：
文献类型：
--
作者：
L. Vaserstein
定理A.设F是一个无限类，n和r是正整数;并且设F的所有那些恰好有r个成员的子类，或者，我们可以说，设F的所有成员的r-组合以任何方式被划分为I i个互斥类Ct {i= 1，2，.，fi），使得每个r-组合都是一个且只有一个Ct的成员;然后，假设选择公理，F必须包含一个无限子类A，使得A的所有成员的r-组合都属于同一个Ct。
Theorem A. Let F be an infinite class, and n and r positive integers; and let all those sub-classes of F which have exactly r members, or, as we may say, let all r-combinations of the members of F be divided in any manner in\i mutually exclusive classes Ct {i= 1, 2,..., fi), so that every r-combination is a member of one and only one C;; then, assuming the Axiom of Selection, F must contain an infinite sub-class A such that all the r-combinations of the members of A belong to the same Ct.