pairwise disjoint

Adjective

 * 1)  Let $$\{A_\lambda\}_{\lambda\in\Lambda}$$ be any collection of sets indexed by a set $\Lambda$.  We call the indexed collection pairwise disjoint if for any two distinct indices, $$\lambda,\mu\in\Lambda$$, the sets $$A_\lambda$$ and $$A_\mu$$ are disjoint.
 * 2) * 2009, John M. Franks, A (Terse) Introduction to Lebesgue Integration,, page 27,
 * For example, if we had a collection of pairwise disjoint intervals of length $$1/2, 1/4, 1/8,\dots 1/2^n,\dots$$,etc., then we would certainly like to be able to say that the measure of their union we is the sum $$\sum 1/2^n=1$$ which would not follow from finite additivity.
 * For example, if we had a collection of pairwise disjoint intervals of length $$1/2, 1/4, 1/8,\dots 1/2^n,\dots$$,etc., then we would certainly like to be able to say that the measure of their union we is the sum $$\sum 1/2^n=1$$ which would not follow from finite additivity.

Usage notes
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.

Synonyms

 * mutually disjoint

Translations

 * Catalan: mútuament disjunts, disjunts dos a dos
 * Dutch: paarsgewijs disjunct, wederzijds disjunct
 * French: disjoints deux à deux, mutuellement disjoints
 * German: paarweise disjunkt
 * Indonesian: saling terlepas
 * Italian: insiemi mutuamente disgiunti, a due a due disgiunti
 * Mandarin: 兩兩不交
 * Spanish: disjuntos por pares, mutuamente disjuntos