The L∞-norm or maximum norm (or uniform norm) is the limit of the Lp-norms for .
defined on the set of all functions on the closure of with values in the Lp space given by the formula
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In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz states that the averages of powers of certain norm-bounded operators on converge in a suitable sense.