2742 INDEX

gauge function, 444Gauss’s formula, 1810Gaussian measure, 2011, 2021Gelfand triple, 1168, 1419, 2365general spherical coordinates, 363generalized gradient

pseudomonotone, 867generalized gradients, 865generalized subgradient

upper semicontinuity, 866Gerschgorin’s theorem, 1667good lambda inequality, 299, 2130Gram determinant, 530Gram matrix, 530Gram Schmidt process, 190Gram Schmidt process., 189Gramm Schmidt process, 87great Picard theorem, 1763

Hadamard three circles theorem, 1658Hahn Banach theorem, 445Hamel basis, 2727Hardy Littlewood maximal function, 933Hardy’s inequality, 417harmonic functions, 1617Haursdorff measures, 993Hausdorff

maximal principle, 2725Hausdorff and Lebesgue measure, 1003, 1005Hausdorff dimension, 1003Hausdorff maximal principle, 36, 343, 389,

444Hausdorff measure

translation invariant, 997Hausdorff measures, 993Hausdorff metric, 175Hausdorff space, 164Heine Borel, 37Heine Borel theorem, 147hemicontinuous, 824, 2525Hermitian, 90higher order derivative

multilinear form, 722higher order derivatives, 721

implicit function theorem, 735

inverse function theorem, 735Hilbert Schmidt operators, 554, 2228Hilbert Schmidt theorem, 538, 663Hilbert space, 517hitting this before that, 2107Holder inequality

backwards, 451Holder space

compact embedding, 206not separable, 204

Holder spaces, 204Holder’s inequality, 186, 399homotopic to a point, 1780Hormander condition, 1124

implicit function theorem, 127, 130, 131, 732,734

higher order derivatives, 735implicit inclusion, 1442inclusions

quasibounded operator, 2653increasing function

differentiability, 946independent events, 1865independent random vectors, 1865independent sigma algebras, 1865indicator function, 232infinite products, 1785inner product space, 517inner regular, 259, 1857, 1988

compact sets, 259inner regular measure, 279integration

with respect to a martingale, 2137integration by parts, 2596integration with respect to martingales

Ito isometry, 2142interior point, 97, 137interpolation inequalities, 1306interpolation inequality, 1510invariance of domain, 218, 769, 770

Brouwer fixed point theorem, 376inverse

left inverse, 76right inverse, 76