364 INDEX p norms, 99 parallelepiped definition, 334 volume, 334 partial derivatives, 147, 155 continuous, 155 partial order, 60 partially ordered set, 60 partition of unity, 84 partitioned matrix, 11 permutation, 35 permutation matrix, 18 permutation symbol, 336 pi systems, 184 piecewise smooth differentiable, 267, 276 pivot column, 27 point of density, 244 pointwise compact, 78 pointwise convergence, 77 pole, 300 Polish space, 68, 233 polynomial in many variables, 117 polynomials, 117 positive linear functional measure, 239 positive part, 205 power set, 49 preserving distance, 16 primitive, 299 product measure, 220 product of matrices inverse, 24 products of Borel sets, 194 Radon measure, 233 Radon Nikodym theorem, 217 Radon Nikodym derivative, 217 rank, 29 rank of a matrix, 44 rank theorem, 173 rational function, 117 real and imaginary parts, 204 regular, 233 measure space, 191, 230 regular values, 304 removable singularity, 301 retract, 224 fixed point property, 224 right handed system, 331 right inverse, 31–33 right polar factorization, 15 rot, 338 row equivalent, 27 row operations, 18 row operations linear relationships, 25 row rank, 44 row reduced echelon form, 26 row reduced echelon form existence, 27 uniqueness, 28 Russell’s paradox, 51 saddle point, 134 Sard’s theorem, 247, 306 scalar field, 338 scalars, 91 Schroder Bernstein theorem, 52 Schur’s theorem, 13 second derivative, 151 second derivative test, 171, 172 sections of open sets, 154 separable metric space Lindeloff property, 68 separated sets, 80 sequence, 64 Cauchy, 65 subsequence, 65 sequentially compact set, 69 series double sum, 56 set F sigma, 233 sets, 49 G delta, 233 sgn, 33 uniqueness, 35 sigma algebra, 179 sign of a permutation, 35 signed measure, 215 Hahn decomposition, 215 signed measures Hahn decomposition, 215