normed vector space


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normed vector space

[′nȯrmd ′vek·tər ′spās]
(mathematics)
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As for a normed vector space to be a CAT([KAPPA]) space, for some [kappa] [member of] R, we have the following result:
([7], [26]) The contingent cone [T.sub.x]D to D at x in the closure D of a subset D of a normed vector space is defined by
A sequence [{[w.sub.l]}.sub.l[member of]N] in a normed vector space V is called a Cauchy sequence, if for every [epsilon] > 0 there exists L [member of] N such that for all integers l, m > L, we have [parallel][w.sub.l] - [w.sub.m][parallel] < [epsilon].
((7)) Let f: E [right arrow] E' be a mapping from a normed vector space E into a Banach space E' subject to the inequality
Let E be a normed vector space. Let us denote by v [right arrow] [[parallel]v[parallel].sub.E] the norm defined on E and let N be the set of natural numbers.
For each sequence M = [([M.sub.n]).sub.n[member of]N] of positive numbers, D(X,M) is a normed vector space. When M = [([M.sub.n]).sub.n[member of]N] is an algebra sequence, then D(X,M) is a normed algebra.
It then moves on to cover the Lebesgue measures, integration on the real line, basic limit theorems, and normed vector spaces. The Lebesgue and Riemann integrals are compared.