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| 003 | OSt | ||
| 005 | 20250125153107.0 | ||
| 008 | 241112s9999 xx 000 0 und d | ||
| 020 |
_a9780821887189 (pbk.) _c₹ 1270.00 |
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| 040 |
_bENG _cIISER-BPR |
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| 041 | _aENG | ||
| 082 |
_a515.42 _bTAY _223rd |
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| 100 |
_aTaylor, Michael _91097 |
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| 222 | _aMathematics | ||
| 245 | 0 | _aMeasure theory and integration | |
| 250 | _a1st ed. | ||
| 260 |
_aRhode Island: _bAmerican Mathematical Society, _cc2012. |
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| 300 |
_axiii, 319p. : _c24cm |
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| 440 |
_aGraduate Studies in Mathematics _vVol. 76 _92623 |
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| 504 | _aIncludes appendices, bibliographic references, symbol index and subject index. | ||
| 520 | _aThis self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to Lp spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to L2 spaces as Hilbert spaces, with a useful geometrical structure. Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope. There are further constructions of measures, including Lebesgue measure on n -dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration of differential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory. | ||
| 650 |
_aMathematics _92624 |
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| 650 |
_aAnalysis _92625 |
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| 650 |
_aTheory of measure and integration _92626 |
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| 650 |
_aMeasure theory _92627 |
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| 650 |
_aIntegration _92628 |
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| 942 |
_cBK _2ddc |
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| 942 | _2ddc | ||
| 947 | _a1270 | ||
| 948 | _a22 | ||
| 999 |
_c4237 _d4237 |
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