(set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.

(mathematical analysis) The supremum (least upper bound) of a function which holds almost everywhere. In symbols, ess sup f= inf M:𝜇(x:f(x)>M)=0