2746 INDEX

operator of penalizationdemicontinuous, 842

operatorsclosed range, 466

optional sampling theorem, 1959order, 1809order of a pole, 1637order of a zero, 1630order of an elliptic function, 1820ordered

partial, 2725totally ordered, 2725

orientable manifold, 1063orientation, 1066orthonormal, 189orthonormal set, 535outer measure, 234, 269outer regular, 259, 1857, 1988outer regular measure, 279

p norms, 187pap97, 1537paracompact space, 421partial derivative, 120partial derivatives, 714, 724

continuous, 724partial order, 35, 444, 2725partially ordered set, 2725partition, 43partition of unity, 287, 426, 1254

metric space, 425, 426penalization operators, 841period parallelogram, 1820permutation, 68Phragmen Lindelof theorem, 1656pivot space, 1168, 1419, 2365Plancherel theorem, 1108point of density, 1244pointwise compact, 154pointwise convergence, 163pointwise limits of measurable functions, 648polar, 1381polar decomposition, 609pole, 1637Polish Space

Kolmogorov Extention, 1862Polish space, 143, 258polish space, 1522polynomial, 195, 1097positive, 560positive and negative parts of a measure, 966positive definite, 2003positive definite functions, 1938positive linear functional, 262, 288power series

analytic functions, 1625power set, 29precompact, 167, 206, 1215, 1443, 2384predictable, 2066, 2439primitive, 1608principal branch of logarithm, 1654principal ideal, 1799probability space, 301, 1856product measure, 324product rule, 1238product topology, 166, 391progressively measurable, 2060, 2250

inclusions, 2640, 2677progressively measurable

composition, 2250integral of, 2062

progressively measurable solutionsnoise, 2640

progressively measurable version, 2065projection in Hilbert space, 520projection map, 841Prokhorov’s theorem, 1992proper, 907properties of integral

properties, 54pseudo continuous, 2003pseudogradient, 811pseudomonotone, 2525

bounded, 850demicontinuous, 826generalized gradient, 867generalized perturbation, 932L pseudomonotone, 923modified bounded, 852, 853monotone and hemicontinuous, 824