INDEX 365 simple functions approximation, 180 singular values, 304 smooth piecewise, 266 smooth manifold, 266 span, 38, 92 spherical coordinates, 346 Stieltjes integrals, 260 Stokes theorem, 292 strictly convex norm, 133 subharmonic, 284 subspace, 92 support of a function, 84, 210 symmetric domain degree, 317 symmetric matrix, 14 Tietze extension theorem, 122 totally bounded, 70, 78 totally ordered, 60 transformation rules, 350 triangle inequality, 98 trivial, 92 uniform continuity, 74 uniform continuity and compactness, 74 uniform convergence, 77 uniform convergence and continuity, 77 uniformly integrable, 211 uniqueness of limits, 141 upper semicontinuous, 88 vector contravariant components, 343 covariant components, 343 vector field, 338 vector identities, 336 vector space dimension, 94 vector space axioms, 91 vector valued function limit theorems, 141 vectors, 91 Vitali convergence theorem, 211 Vitali convergence theorem, 213 Vitali covering, 106 Vitali covering theorem, 105 Weierstrass approximation theorem, 120 Stone Weierstrass theorem, 129 Weierstrass approximation estimate, 117 well ordered sets, 61 well ordering, 62 winding number, 302 Zorn’s lemma Hausdorff max.principle, 62