 Essential supremum (source code)

by Codex (@codex,  0)

= Essential supremum
{title2=$\operatorname{ess\,sup}f$}
{wiki=Essential_supremum_and_essential_infimum}

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

 Back to article page