INDEX 2741
inequality property, 835projection map, 841strict monotone inequality, 839strictly monotone, 836, 837
duality mapping, 832, 2531duality maps, 476
application of duality, 832, 2531properties, 834, 2532
Eberlein Smulian theorem, 465Egoroff theorem, 232, 243eigenvalues, 77, 1668, 1671Ekeland variational principle, 507elementary factors, 1789elementary function, 2137, 2229elementary function
integral, 2229elementary functions, 2229elementary set, 397elementary sets, 321elliptic, 1819entire, 1631epsilon net, 144, 150equality of mixed partial derivatives, 127,
727equi integrable, 639, 2157equicontinuous, 154, 691equivalence class, 35equivalence relation, 35ergodic, 306
individual ergodic theorem, 302Erling’s lemma, 1215, 1443, 2384essential singularity, 1637essentially more slowly, 986Euler’s theorem, 1815events, 1865evolution equation
continuous semigroup, 585exchange theorem, 62, 179exponential growth, 1116extended complex plane, 1599extending off closed set, 427extension theorem, 1292extention
mapping, 427
Fatou’s lemma, 248filtration, 2060filtration
normal, 2060finite intersection property, 148, 168finite measure
regularity, 260, 1859finite measure space, 223first hitting time, 2081fixed point property, 368, 372, 433, 801fixed point theorem
Cariste, 509Kakutani, 846, 1565
fixed pointsmeasurability, 1553
Fourier seriesuniform convergence, 475
Fourier transform L1, 1105fractional linear transformations, 1738, 1743
mapping three points, 1740fractional powers
sectorial operator, 1719fractional spaces
reflexive, 1508Frechet derivative, 116, 711Fredholm alternative, 559Fredholm operator
Banach space, 471Fresnel integrals, 1694Fubini’s theorem, 315, 324, 333
Bochner integrable functions, 667function, 32
uniformly continuous, 37function element, 1749, 1848functional equations, 1838functions of Wiener processes, 2311fundamental theorem of algebra, 1632fundamental theorem of calculus, 56, 935,
936general Radon measures, 1083Radon measures, 1081
Gamma function, 417, 1005gamma function, 1809Gateaux derivative, 714, 716