Index
a-primitive, of a function, 56, 276
a.e., almost everywhere, 30
Abel, Niels H., 269
summation formula, 168
Test, for integrals, 269
Test, for series, 168
Absolute continuity, of indefinite in-
tegrals, 161, 336, 356
of a charge or measure, 340
for a function, 231, 295, 402, 409
uniform, 178, 246, 356
Absolute integrability, characteriza-
tion of, 104, 281
comparison test for, 107
of a function, 37, Section 7 (esp.
101), 258
Absolutely convergent series,
space of, 147, 166
ACs,ACGs function, 243
Additivity, of the integral over inter-
vals, 44
of the measure function, 302
Algebra, of sets, 318
Almost everywhere, definition, 30
Almost uniform,
Cauchy sequence, 172, 347
convergence, 171, 347
Antiderivative, of a function, 56
Approximation Theorem, for sets,
312-315
Arcsine function, 71
Arctangent function, 71
Lemma, 373
Arzela, Cesare, 116
Arzela-Young Theorem, 165
Ascoli, Giulio, 7
Baire, Rene, 320
Category Theorem, 320
Ball, closed, 4
open, 4
Banach, Stefan, 239, 407
Banach-Zarecki Theorem, 239
Base point, of an indefinite integral,
56, 276
Beta function, 95, 222
Bielawski, Marie, 217
Bonnet Mean Value Theorem,
194, 204
Borel sets, 311
Borel-Cantelli Lemma, 156, 306, 362
Botsko, Michael W., 163
Bounded interval, 4
sequences, space of, 146
variation, function, 103, 294, 402,
408
sequences, 166
c-primitive, of a function, 56, 63 ff.,
276
c.e., countably many exceptions, 30
449
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