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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

Second-Order Necessary Conditions for Set Constrained Nonsmooth Optimization Problems via Second-Order Projective Tangent Cones

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].

Centralizers of the infinite symmetric group

((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

Stability of additive mappings in generalized normed spaces

where v belongs to some normed vector space V of functions defined on [0;1].

On chaotic and stable behaviour of the von Foerster-Lasota equation in some Orlicz spaces/von Foersteri-Lasota vorrandite kaootilisest ja stabiilsest kaitumisest Orliczi ruumides

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.

Perturbation of parallel asynchronous linear iterations by floating point errors

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.

Algebrability of some subsets of the disk 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.

Real Analysis: Measure and Integration