INDEX 363

singular values, 302smooth

piecewise, 264smooth manifold, 264span, 38, 92spherical coordinates, 344Stieltjes integrals, 257Stokes theorem, 290strictly convex

norm, 133subharmonic, 282subspace, 92support of a function, 84, 212symmetric domain

degree, 315symmetric matrix, 14

Tietze extension theorem, 122totally bounded, 70, 78totally ordered, 60transformation rules, 348triangle inequality, 98trivial, 92

uniform continuity, 74uniform continuity and compactness, 74uniform convergence, 77uniform convergence and continuity, 77uniformly integrable, 214uniqueness of limits, 141upper semicontinuous, 89

vectorcontravariant components, 341covariant components, 341

vector field, 336vector identities, 334vector space

dimension, 94vector space axioms, 91vector valued function

limit theorems, 141vectors, 91Vitali

convergence theorem, 214Vitali convergence theorem, 216Vitali covering, 106Vitali covering theorem, 105

Weierstrassapproximation theorem, 120Stone Weierstrass theorem, 129

Weierstrass approximationestimate, 117

well ordered sets, 61well ordering, 62winding number, 300

Zorn’s lemmaHausdorff max.principle, 62