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020 _a9783319225067
_9978-3-319-22506-7
024 7 _a10.1007/978-3-319-22506-7
_2doi
035 _ato000560624
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA312-312.5
072 7 _aPBKL
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.42
_223
100 1 _aKubrusly, Carlos S.
_eauthor.
_9467614
245 1 0 _aEssentials of Measure Theory
_helectronic resource
_cby Carlos S. Kubrusly.
250 _a1st ed. 2015.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXIII, 279 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
505 0 _aPreface -- Part I. Introduction to Measure and Integration.-1. Measurable Functions -- 2. Measure on a σ-Algebra -- 3. Integral of Nonnegative Functions -- 4. Integral of Real-Valued Functions -- 5. Banach Spaces Lp -- 6. Convergence of Functions -- 7. Decomposition of Measures -- 8. Extension of Measures -- 9. Product Measures -- Part II -- 10. Remarks on Integrals -- 11. Borel Measure -- 12. Representation Theorems -- 13. Invariant Measures -- References -- Index.
520 _aClassical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an “abstract” approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgue integral are presented as an important particular case of general theory. Part II of the text is more advanced and is addressed to a more experienced reader. The material is designed to cover another one-semester graduate course subsequent to a first course, dealing with measure and integration in topological spaces. The final section of each chapter in Part I presents problems that are integral to each chapter, the majority of which consist of auxiliary results, extensions of the theory, examples, and counterexamples. Problems which are highly theoretical have accompanying hints. The last section of each chapter of Part II consists of Additional Propositions containing auxiliary and complementary results. The entire book contains collections of suggested readings at the end of each chapter in order to highlight alternate approaches, proofs, and routes toward additional results. With modest prerequisites, this text is intended to meet the needs of a contemporary course in measure theory for mathematics students and is also accessible to a wider student audience, namely those in statistics, economics, engineering, and physics. Part I may be also accessible to advanced undergraduates who fulfill the prerequisites which include an introductory course in analysis, linear algebra (Chapter 5 only), and elementary set theory.
650 0 _amathematics.
_9566183
650 0 _aMeasure theory.
_9461133
650 0 _aTopology.
_9303685
650 1 4 _aMathematics.
_9566184
650 2 4 _aMeasure and Integration.
_9303749
650 2 4 _aTopology.
_9303685
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-22506-7
912 _aZDB-2-SMA
999 _c415269