Real and Complex Analysis (Rudin)

INDEX 411
Double integral, 165
Dual space, 108, 112, 127, 130
Eberlein, W. F., 58
Edwards, R. E., 398
Egoroff's theorem, 73
Elementary factor, 301
Elementary set, 161
Ellipse, 287
Ellis, H. W., 399
Empty set, 6
End point, 200
Entire function, 198
Equicontinuous family, 245
Equivalence classes, 67
Equivalent paths, 201
Essential range, 74
Essential singularity, 211, 267
Essential supremum, 66
Euclidean space, 34, 49
Euclid's inequality, 77
Euler's identity, 2
Exponential function, 1, 198
Exponential type, 372, 382, 383
Extended real line, 7, 9
Extension, 105
Extensiop theorem, 105
Extremal function, 255
Extreme point, 251
Fa-set, 12
Factorization, 303, 338, 344
Family, 6
Fatou, P., 400
Fatou's lemma, 23, 68, 309, 344
Fatou's theorem, 249
Fejer kernel, 252
Fejer's theorem, 91
Field,394
Finite additivity, 17
First category, 98
Fixed point, 151,229,247,293,297,314,318,395
Ford, L. R., 401
Fourier coefficients, 82, 91
of measure, 133
Fourier series, 83,91
Fourier transform, 178
Fubini's theorem, 164, 168
Function, 7
absolutely continuous, 145
analytic, 197
Borel,13
bounded,66
of bounded variation, 148
complex, 8
continuous, 8
convex, 61
entire, 198
essentially bounded, 66
exponential, 1
of exponential type, 372, 383
harmonic, 232
holomorphic, 197
Lebesgue integrable, 24
left-continuous, 157
locally integrable, 194
lower semicontinuous, 37
measurable, 8, 29
meromorphic, 224
modular, 328
nowhere differentiable, 114
rational, 267
real,8
simple, 15
subharmonic, 335
summable, 24
upper semicontinuous, 37
Function element, 323
Functional:
bounded,96
on Co, 130
complex-linear, 105
continuous, 96
on Hilbert space, 81
on n, 127
linear, 33
multiplicative, 191, 364
positive, 34
real-linear, 105
Functional analysis, 108
Fundamental domain, 329
Fundamental theorem of calculus, 144, 148
G,-set, 12
Gap series, 276, 321, 334, 354, 385
Gelfand, I., 402
Gelfand-Mazur theorem, 359
Gelfand transform, 370
Geometric mean, 63
Goursat, E., 400
Graph, 114, 174
Greatest lower bound, 7
Green's theorem, 389
Hadamard, J., 264, 321
Hahn-Banach theorem, 104, 107,270,313,359
Hahn decomposition, 126
Hall, D., 398