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008 160505s2016 gw |||| o |||| 0|eng
010 _a 2019740033
020 _a9783319307442
024 7 _a10.1007/978-3-319-30744-2
_2doi
035 _a(DE-He213)978-3-319-30744-2
040 _aDLC
_beng
_epn
_erda
_cDLC
072 7 _aPBKB
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKB
_2thema
082 0 4 _a515.8
_223
100 1 _aLoeb, Peter A.
_eauthor.
245 1 0 _aReal Analysis /
_cby Peter A. Loeb.
250 _a1st ed. 2016.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2016.
300 _a1 online resource (XII, 274 pages)
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- Set Theory and Numbers -- Measure on the Real Line -- Measurable Functions -- Integration -- Differentiation and Integration -- General Measure Spaces -- Introduction to Metric and Normed Spaces -- Hilbert Spaces -- Topological Spaces -- Measure Construction -- Banach Spaces -- Appendices -- References.
520 _aThis textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors. The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach. The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics.
588 _aDescription based on publisher-supplied MARC data.
650 0 _aFunctions of real variables.
650 0 _aFunctional analysis.
650 0 _aMeasure theory.
650 1 4 _aReal Functions.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12171
650 2 4 _aFunctional Analysis.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12066
650 2 4 _aMeasure and Integration.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12120
776 0 8 _iPrinted edition:
_z9783319307428
776 0 8 _iPrinted edition:
_z9783319307435
776 0 8 _iPrinted edition:
_z9783319808796
906 _a0
_bibc
_corigres
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942 _2ddc
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