Index

Ho, 112

A®B, 210

a.e., 125

absolutely continuous

- complex measure, 366

- function, 176

- measure, 311

- signed measure, 356, 359

aleph-nought, 391

algebra, 55

- generated, 57

almost everywhere, 125

almost uniformly convergent, 250

analytic set, 112

antiderivative, 30

approximate identity, 291

Archemedes, 30

arrangement, 387

Arzela's theorem, 40, 157

BR,

95

3*1,211

£x,8 2

Baire, Rene, 44

Banach

- algebra with identity, 290

- algebra, commutative, 290

- lattice, 365

- spaces, 266

Bernoulli, Daniel, 31

Bessel's inequality, 298, 308

binomial distribution, 69

Borel, Emile, 44

Borel

- measurable function, 227

- subsets, 95, 102

-subsets of M2, 211

bounded

- convergence theorem, 151

- linear functional, 302, 375

- variation, 397

C, 243

C(R), 162

C[a,b], 41, 160

C°°[a,6], 167

C°°-function, 286

C°°(1R) , 164

C°°(U), 286

C~(t/) , 286

C

1

-mapping, 403

Co (M"), 295

CC(R), 162

C

c

(R

n

), 280, 295

C n E, 56

c, 112

X

A

(x), 30

Cantor sets, 23, 24

Cantor's ternary set, 25

Carat heodory, Constant in, 44

cardinal number, 391

cardinality

- of a set, 391

- of the continuum, 112, 391

Cartesian product, 389

Cauchy, Augustein-Louis, 31

Cauchy in measure, 259

Cauchy-Schwartz inequality, 264, 296

chain rule, 204

change of variable for Riemann integration,

200, 207

change of variable formula

413