INDEX 919

differentiable, 267multi - index, 130multi-index, 194, 375multi-index notation, 194multifunction

strongly measurable, 273multifunctions, 271

measurability, 271Muntz theorem, 153

negative part, 285Neuman series, 205Newton’s method, 201no retract onto boundary of ball, 421non equal mixed partials

example, 199norm

p norm, 106normal, 405, 759, 773normal filtration, 817normal topological space, 503Normed linear space, 106nowhere differentiable functions, 569nuclear operator, 590

one dimensional Stieltjes measure, 294one point compactification, 506open ball, 71

open set, 71open cover, 76, 504open mapping theorem, 536open set, 71open sets, 501

countable basis, 75operator norm, 534optional sampling theorem, 798ordered

partial, 68totally ordered, 68

oriented atlas, 396orthonormal, 108orthonormal set, 584outer measure, 244

measurable, 245total variation, 622

outer measure on real line, 250outer regular, 253, 717

G delta and F sigma sets, 255

outer regularity, 257

p norms, 107paracompact space, 705parallelogram identity, 619partial derivatives, 189, 196

continuous, 197partial order, 68partially ordered set, 68partition

one dimension, 348partition of unity, 92, 512, 709

metric space, 708, 710partitioned matrix, 17permutation, 41permutation matrix, 24pi systems, 243pivot column, 33Plancherel theorem, 383, 384point of density, 326pointwise compact, 86pointwise convergence, 85polar coordinates

integral, 340polar decomposition, 625Polish space, 76, 252polynomial, 375

in many variables, 130polynomials, 130positive, 595positive linear functional, 315, 516

measure, 318positive part, 285positive self adjoint

products, 595roots, 596

power set, 57precompact, 504, 521predictable, 823preserving distance, 22primitive, 224prior, 796prior sets, 836probability distribution function, 250probability space, 715product measure, 306

regular, 306product of matrices