 Now assume in addition that formula_14 is a measure space and, for simplicity, assume that the function formula_4 is measurable.A number formula_16 is called an "essential upper bound" of "f" if the measurable set formula_17 is a set of measure zero, i.e., if formula_18 for "almost all" formula_19 in formula_20.Let

be the set of essential upper bounds.