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