Pairwise disjoint or disjoint? I am reading Lebesgue measure. In many situations I have found that the author says pairwise disjoint collection of subsets of $\mathbb{R}$ and in some others simply disjoint. What is the difference in Mathematics?

A set (of sets) $\mathcal{A}$ is disjoint if $\bigcap \mathcal{A} = \emptyset$.
The set $\mathcal{A}$ is pairwise disjoint when $\forall x \in A: \forall y \in A: x \neq y \implies x \cap y = \emptyset$. This implies disjoint if $|\mathcal{A}| \ge 2$.
So $\mathcal{A} = \{x,y\}$ is disjoint iff it is pairwise disjoint.
But in measure theory, disjoint is often used as a shorthand for "pairwise disjoint".
