 Essential supremum

The essential supremum of a measurable function is the least number $M$ such that $f\le M$ almost everywhere. It equals the $L^{\infty }$ norm for a nonnegative function and, on a finite measure space, $\Vert f{\Vert }_p\to \Vert f{\Vert }_{\infty }$ as $p\to \infty$.