INDEX 2749

strong law of large numbers, 1881, 1982strongly measurable, 643subbasis, 389subgradient

convex lower semicontinuous, 909maximal monotone, 911surjective, 910

subgradientssum, 912

submartingale, 1948submartingale convergence theorem, 1951

continuous case, 2104subspace, 61, 178sum

maximal monotone and pseudomono-tone, 891

sumsindependent, 1875, 1879, 1974

supermartingale, 1948support of a function, 287Suslin space, 1522symmetric derivative

existence, 1091measurable, 1091Radon measure, 1090upper and lower, 1090

symmetric domaindegree, 768

tail event, 1874Tietze extension theorem, 157tight, 1919, 1926, 1990

measures, 1926topological space, 164topological vector space dual, 481total variation, 603, 938totally bounded set, 144totally ordered, 2725trace, 553trajectories, 2049translation invariant, 341translations, 1738triangle inequality, 185, 401triangulated, 208triangulation, 208

trivial, 61, 178Tychanoff fixed point theorem, 503type M, 826, 2527

demicontinuous, 2529demicontinuous, 829sum of linear and type M, 827surjective, 830

uniform boundedness theorem, 439uniform continuity, 161uniform continuity and compactness, 162uniform contraction principle, 160uniform convergence, 163, 1598uniform convergence and continuity, 163uniform convexity, 477uniformly bounded, 149, 691, 1761uniformly continuous, 37uniformly equicontinuous, 149, 1761uniformly integrable, 256, 418unimodular transformations, 1822uniqueness of limits, 707upcrossing, 1949, 1971upper and lower sums, 43upper semi continuity

set valued map, 844upper semicontinuity

set valued map, 844upper semicontinuous

onto, 849upper semicontinuous composition, 844Urysohn’s lemma, 282

variational inequalities with respect to set val-ued map, 2638

variational inequality, 520non-constant convex set, 1568sum of set valued pseudomonotone maps,

1568vector measures, 602, 678vector space

dimension, 181vector space axioms, 177vector valued function

limit theorems, 707vectors, 177