For a function in this set, its essential supremum serves as an appropriate norm:
2.
Thus, the essential supremum and the essential infimum of this function are both 2.
3.
The essential supremum form was given in.
4.
By the definition of " } } as the essential supremum of & thinsp; and the assumption " > 0 } }, we have.
5.
Similarly one can form the space of essentially bounded functions, with the norm given by the essential supremum, and the positive elements of the dual of this space are given by bounded contents that vanish on sets of measure 0.
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