INDEX 913

Binet Cauchy formula, 45block matrix, 15block multiplication, 15, 17Bochner integrable, 655Borel

measure, 248Borel Cantelli lemma, 242, 715Borel measure

metric space, 248Polish space, 256

Borel regular, 447Borel sets, 252Borsuk, 423Borsuk Ulam theorem, 425Borsuk’s theorem, 421bounded continuous linear functions, 534bounded linear maps, 205

continuity, 126bounded set, 110Brouwer fixed point theorem, 329, 420, 578

complact convex set, 163Browder’s lemma, 178, 278, 619Burkholder Davis Gundy

inequality, 877Burkholder Davis Gundy inequality, 875

Cantor function, 269Cantor set, 268Caratheodory extension theorem, 525Caratheodory functions, 274Caratheodory’s procedure, 246Cariste fixed point theorem, 172Cauchy Schwarz inequality, 104, 575Cauchy sequence, 73Cayley Hamilton theorem, 53central limit theorem, 778chain, 68chain rule, 188change of variables, 467

linear map, 330linear maps, 331

characteristic function, 750characteristic polynomial, 53Clairaut’s theorem, 198Clarkson

inequalities, 551Clarkson inequalities, 552Clarkson inequality

p≥ 2, 548easy one, 549

closed disk, 110closed graph theorem, 539closed set, 72, 502closed sets

limit points, 72closure of a set, 74, 75, 503coarea formula, 462, 463cofactor, 47cofactor identity, 201, 414column rank, 50compact map

finite dimensional approximation, 163compact set, 76, 504compactness

closed interval, 109equivalent conditions, 78

completely separable, 75complex

measure, 621complex valued measurable functions, 284components of a vector, 101conditional expectation, 781

Banach space, 701independence, 784

connected, 88open balls, 90, 144

connected component, 89boundary, 410

connected components, 89equivalence class, 89equivalence relation, 89open sets, 90

connected setcontinuous function, 91, 145continuous image, 88

connected setsintersection, 88intervals, 89real line, 89union, 88

continuityalgebraic properties, 129bounded linear maps, 126coordinate maps, 127uniform, 82

continuity of translation, 365