Uniform Norm

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. n mathematical analysis, the uniform norm assigns to real- or complex-valued bounded functions f defined on a set S the nonnegative number |f|_infty=|f|_{infty,S}=supleft{,left|f(x)right|:xin S,right}. This norm is also called the supremum norm, the Chebyshev norm, or the infinity norm. If we allow unbounded functions, this formula does not yield a norm or metric in a strict sense, although the obtained so-called extended metric still allows one to define a topology on the function space in question. If f is a continuous function on a closed interval, or more generally a compact set, then it is bounded and 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.

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Pagina's: 76, Paperback, Betascript Publishers