2740 INDEX

convex hull, 207, 427convex lower semicontinuous

approximation, 915domain and domain of subgradient, 915

convex sets, 483convolution, 412, 1113convolution of measures, 1903coordinate map, 191coordinates, 207countable, 33counting zeros, 1663covariation, 2127cowlicks, 772Cramer’s rule, 77cycle, 1642cylinder sets, 2029cylindrical set, 1870, 1896

Darboux, 57Darboux integral, 57definition of Lp, 402degenerate inclusions

measurable, 2631degenerate inclusions with extra stochastic

integral added, 2633, 2676degenerate operators identities, 2612degree

Leray Schauder, 793demicontinuous, 826, 842, 2526density of continuous functions in Lp, 407derivative

chain rule, 712continuous, 712continuous Gateaux derivatives, 716Frechet, 711Gateaux, 714, 716generalized partial, 723higher order, 721, 722matrix, 714partial, 723second, 721well defined, 711

derivative of inverse, 219derivatives, 117, 711determinant, 69

alternating property, 71cofactor expansion, 74expansion along row (column), 74matrix inverse formula, 75product, 73transpose, 71

differentiable, 711continuous, 712continuous partials, 724locally Lipschitz, 1014

differential equations, 746global existence, 504

differential form, 1065derivative, 1068integral, 1066

differential forms, 1064differentiation

Radon measures, 963, 1090dilations, 1738dimension of a vector space, 181Dini derivates, 946, 971directional derivative, 716distance, 137distribution, 942, 1232, 1856distribution function, 297, 971, 1120distributional derivative, 1163, 1415, 2361distributions

vector valued, 1163, 1415, 2361divergence theorem, 1030DL, 2157domain

subgradient of convex function, 1380dominated convergence theorem, 254, 671Doob

approximation lemma, 2233Doob Dynkin lemma, 1868Doob estimate, 1953Doob Meyer decomposition, 2165Doob’s submartingale estimate, 2070dot product, 183doubly periodic, 1819dual space, 448duality map

strictly monotone, 2534demicontinuous, 834