This norm is also called the supremum norm or the Chebyshev norm. If f is a continuous function on a closed interval, or more generally a compact set, then the supremum in the above definition is attained by the Weierstrass extreme value theorem, so we can replace the supremum by the maximum. In this case, the norm is also called the maximum norm.
The occasion for the subscript "∞" is that
where
where D is the domain of f.
The binary function
is then a metric on the space of all bounded functions on a particular domain. A sequence { fn : n = 1, 2, 3, ... } converges uniformly to a function f if and only if
For complex continuous functions over a compact space, this turns it into a C* algebra.
Uniformity, and thus certainty of the law can only be achieved through uniform interpretation and application, which require the person dealing with the convention to interpret it autonomously, which means detached from his national legal context.
Thus, uniformity of the law concerning the applicable rate of interest is fairly desirable and even necessary to promote the actual raison d'être of the Convention, namely the unification of the sales law within one internationally applicable body of law.
Uniform Law on the International Sale of Goods and the Uniform Law on the Formation of Contracts for the International Sale of Goods, both signed at the UN Hague Diplomatic Conference on the 1st of July 1964, reprinted in (1972) UNTS 107 and in (1972) 834 UNTS 169.
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