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