INDEX 915

Eberlein Smulian theorem, 560Eggoroff theorem, 291Egoroff theorem, 654eigenvalue, 233eigenvalues, 53Ekeland variational principle, 170elementary function, 883, 893elementary functions

linear space, 893elementary matrices, 24embedding into its double dual space, 545equality of mixed partial derivatives, 200equi-integrable, 293equicontinuous, 86, 690equivalence class, 63equivalence relation, 63events, 720evolution equation

continuous semigroup, 610exchange theorem, 101expectation, 722

products of random variables, 723exponential growth, 391extending off closed set, 711extention

mapping, 711extreme values theorem, 82

F sigmaset, 253

Faddeyev, 310Fatou’s lemma, 283Fick’s law, 406filtration, 817filtration

normal, 817finding the inverse, 37finite intersection property, 504finite measure

regularity, 255, 717first hitting time, 796

closed set, 838open set, 838

fixed point property, 329, 434fixed point theorem

Cariste, 172Kakutani, 169

flip, 224

Fourier and inverse Fourier transforms, 379Fourier series

uniform convergence, 571Fourier transform

L1, 381L2, 383continuous, 381convolution, 382, 388in G ∗, 378of functions in G, 376convolution, 386

Fourier transform L1, 381Fourier transforms

polynomial growth, 380Frechet derivative, 186Fredholm operator

Banach space, 564Fubini’s theorem, 306

Bochner integrable functions, 669general product measures, 305

function, 60functions

measurable, 237fundamental theorem of calculus

general Radon measures, 325Radon measures, 324

G delta, 253Gamma function, 372, 452gamma function, 204Gateaux

derivative, 437Gateaux derivative, 189, 191

continuous, 193gauge function, 540Gauss Jordan method for inverses, 37generalized normal distribution, 762geometric mean, 233good lambda inequality, 299, 874Gram Schmidt process, 109Gram Schmidt process., 108graph of a linear map, 538Green’s theorem, 497

Hahndecomposition, 301

Hahn Banach theorem, 541complex version, 542