| 000 | 03638nam a22004575i 4500 | ||
|---|---|---|---|
| 001 | 978-0-8176-4656-1 | ||
| 003 | DE-He213 | ||
| 005 | 20160302164305.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2009 xxu| s |||| 0|eng d | ||
| 020 |
_a9780817646561 _9978-0-8176-4656-1 |
||
| 024 | 7 |
_a10.1007/978-0-8176-4656-1 _2doi |
|
| 050 | 4 | _aQA299.6-433 | |
| 072 | 7 |
_aPBK _2bicssc |
|
| 072 | 7 |
_aMAT034000 _2bisacsh |
|
| 082 | 0 | 4 |
_a515 _223 |
| 100 | 1 |
_aBenedetto, John J. _eauthor. |
|
| 245 | 1 | 0 |
_aIntegration and Modern Analysis _h[electronic resource] / _cby John J. Benedetto, Wojciech Czaja. |
| 264 | 1 |
_aBoston : _bBirkhäuser Boston, _c2009. |
|
| 300 |
_aXIX, 575 p. 24 illus. _bonline resource. |
||
| 336 |
_atext _btxt _2rdacontent |
||
| 337 |
_acomputer _bc _2rdamedia |
||
| 338 |
_aonline resource _bcr _2rdacarrier |
||
| 347 |
_atext file _bPDF _2rda |
||
| 490 | 1 | _aBirkhäuser Advanced Texts / Basler Lehrbücher | |
| 505 | 0 | _aClassical Real Variables -- Lebesgue Measure and General Measure Theory -- The Lebesgue Integral -- The Relationship between Differentiation and Integration on -- Spaces of Measures and the Radon#x2013;Nikodym Theorem -- Weak Convergence of Measures -- Riesz Representation Theorem -- Lebesgue Differentiation Theorem on -- Self-Similar Sets and Fractals -- Functional Analysis -- Fourier Analysis. | |
| 520 | _aA paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolute continuity on differentiation and integration. This leads to fundamental results such as the Dieudonné–Grothendieck theorem and other intricate developments dealing with weak convergence of measures. Key Features: Fascinating historical commentary interwoven into the exposition; Hundreds of problems from routine to challenging; Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent study projects; Two significant appendices on functional analysis and Fourier analysis. Key Topics: In-depth development of measure theory and Lebesgue integration; Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of state-of-the-art results; Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals; Evolution of the Riesz representation theorem to Radon measures and distribution theory; Deep results in modern differentiation theory; Systematic development of weak sequential convergence inspired by theorems of Vitali, Nikodym, and Hahn–Saks; Thorough treatment of rearrangements and maximal functions; The relation between surface measure and Hausforff measure; Complete presentation of Besicovich coverings and differentiation of measures. Integration and Modern Analysis will serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study. | ||
| 650 | 0 | _aMathematics. | |
| 650 | 0 | _aMathematical analysis. | |
| 650 | 0 | _aAnalysis (Mathematics). | |
| 650 | 1 | 4 | _aMathematics. |
| 650 | 2 | 4 | _aAnalysis. |
| 700 | 1 |
_aCzaja, Wojciech. _eauthor. |
|
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9780817643065 |
| 830 | 0 | _aBirkhäuser Advanced Texts / Basler Lehrbücher | |
| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-0-8176-4656-1 |
| 912 | _aZDB-2-SMA | ||
| 999 |
_c184199 _d184199 |
||