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Wiktionary英語版での「pairwise disjoint」の意味 |
pairwise disjoint
形容詞
pairwise disjoint (not comparable)
- (mathematics, set theory, of a collection of two または more sets) Let be any collection of sets indexed by a set
Λ
{\displaystyle \Lambda }
. We call the indexed collection pairwise disjoint if for any two distinct indices, , the sets and are disjoint.
- 2007, Pierre Antoine Grillet, Abstract Algebra, Springer, 2nd Edition, page 61,
- Proposition 4.5. Every permutation is a product of pairwise disjoint cycles, and this decomposition is unique up to the order of the terms.
- 2009, John M. Franks, A (Terse) Introduction to Lebesgue Integration, American Mathematical Society, page 27,
- For example, if we had a collection of pairwise disjoint intervals of length ,etc., then we would certainly like to be able to say that the measure of their union we is the sum which would not follow from finite additivity.
- 2015, Su Gao, Stephen C Jackson, Brandon Seward, Group Colorings and Bernoulli Subflows, American Mathematical Society, page 158,
- 2007, Pierre Antoine Grillet, Abstract Algebra, Springer, 2nd Edition, page 61,
使用する際の注意点
The condition is a generalization of the concept of disjoint sets, from two to an arbitrary collection of sets. When applied to a collection, the original formulation - that the sets have an intersection equal to the empty set - becomes ambiguous and in need of clarification.
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