Real AnalysisCambridge University Press, 15.08.2000 - 401 Seiten This course in real analysis is directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something of value to specialists and nonspecialists alike. The text covers three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal, down-to-earth style, the author gives motivation and overview of new ideas, while still supplying full details and complete proofs. He provides a great many exercises and suggestions for further study. |
Inhalt
III | 3 |
IV | 14 |
V | 17 |
VI | 18 |
VII | 25 |
VIII | 31 |
IX | 34 |
X | 36 |
LII | 202 |
LIII | 210 |
LIV | 212 |
LV | 214 |
LVI | 215 |
LVII | 221 |
LVIII | 225 |
LIX | 232 |
XI | 37 |
XII | 39 |
XIII | 43 |
XIV | 45 |
XV | 49 |
XVI | 51 |
XVII | 53 |
XVIII | 60 |
XIX | 62 |
XX | 63 |
XXI | 69 |
XXII | 73 |
XXIII | 78 |
XXIV | 87 |
XXV | 89 |
XXVI | 92 |
XXVII | 97 |
XXVIII | 102 |
XXIX | 106 |
XXX | 108 |
XXXI | 114 |
XXXII | 120 |
XXXIII | 126 |
XXXIV | 128 |
XXXV | 131 |
XXXVI | 136 |
XXXVII | 137 |
XXXVIII | 139 |
XXXIX | 143 |
XL | 150 |
XLI | 153 |
XLII | 160 |
XLIII | 162 |
XLIV | 170 |
XLV | 176 |
XLVI | 178 |
XLVII | 183 |
XLVIII | 185 |
XLIX | 188 |
L | 194 |
LI | 201 |
LX | 234 |
LXI | 239 |
LXII | 242 |
LXIII | 244 |
LXIV | 250 |
LXV | 254 |
LXVI | 257 |
LXVII | 258 |
LXVIII | 261 |
LXIX | 263 |
LXX | 268 |
LXXI | 274 |
LXXII | 277 |
LXXIII | 283 |
LXXIV | 289 |
LXXV | 292 |
LXXVI | 293 |
LXXVII | 296 |
LXXVIII | 302 |
LXXIX | 304 |
LXXX | 306 |
LXXXI | 310 |
LXXXII | 312 |
LXXXIII | 314 |
LXXXIV | 322 |
LXXXV | 328 |
LXXXVI | 333 |
LXXXVII | 335 |
LXXXVIII | 337 |
LXXXIX | 342 |
XC | 350 |
XCI | 352 |
XCII | 356 |
XCIII | 359 |
XCIV | 370 |
XCV | 377 |
| 379 | |
XCVII | 395 |
XCVIII | 397 |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
a₁ AC[a algebra Borel set bounded variation BV[a Cantor function Cantor set Cauchy sequence Chapter closed sets complete consider contains continuous function converges in measure converges pointwise converges uniformly Corollary define dense differentiable equicontinuous equivalent example Exercise exists fact finite fn(x follows Fourier series function f ƒ ƒ ƒ is continuous given ɛ hence Hint homeomorphic inequality infinite integrable functions L₁ lattice Lebesgue integral Lebesgue measurable Lebesgue's Lemma Let f lim inf lim sup limit Lipschitz measurable functions measurable sets monotone nonempty nonnegative normed vector space notation null set open intervals open sets pairwise disjoint partition Ra[a real numbers real-valued functions Riemann integrable Riesz satisfies show that ƒ simple functions step function subalgebra subset subspace suppose that ƒ totally bounded trig polynomial uncountable uniform convergence uniformly continuous π π
Verweise auf dieses Buch
Research in Collegiate Mathematics Education VI Fernando Hitt,Guershon Harel,Annie Selden Keine Leseprobe verfügbar - 2006 |