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The essential supremum is defined as the infimum (greatest lower bound) of the set of all essential upper bounds of the function's absolute value.

Conditions: f is a measurable function on E.; M ranges over all real numbers such that |$f(x)$| $\leqslant M$ holds almost everywhere on E.

The essential supremum is defined as the infimum (greatest lower bound) of the set of all essential upper bounds of the function's absolute value.

Conditions: f is a measurable function on E.; M ranges over all real numbers such that |$f(x)$| $\leqslant M$ holds almost everywhere on E.