000			04702nam a2200349Ki 4500
001			ocn855534519
003			OCoLC
005			20240726105323.0
008			130812s2000 enka ob 001 0 eng d
040			_aNT _beng _erda _cNT
020			_a9781139648714 _q((electronic)l(electronic)ctronic)l((electronic)l(electronic)ctronic)ctronic bk.
050	0	4	_aQA300 _b.R435 2000
049			_aNTA
100	1		_aCarothers, N. L., _d1952- _e1
245	1	0	_aReal analysisN.L. Carothers.
260			_aCambridge [UK] ; _aNew York : _bCambridge University Press, _c(c)2000.
300			_a1 online resource (xiii, 401 pages) : _billustrations.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_adata file _2rda
504			_a2
505	0	0	_tMetric Spaces -- _tCalculus Review -- _tReal Numbers -- _tLimits and Continuity -- _tCountable and Uncountable Sets -- _tEquivalence and Cardinality -- _tCantor Set -- _tMonotone Functions -- _tMetrics and Norms -- _tMetric Spaces -- _tNormed Vector Spaces -- _tMore Inequalities -- _tLimits in Metric Spaces -- _tOpen Sets and Closed Sets -- _tOpen Sets -- _tClosed Sets -- _tRelative Metric -- _tContinuity -- _tContinuous Functions -- _tHomeomorphisms -- _tSpace of Continuous Functions -- _tConnectedness -- _tConnected Sets -- _tCompleteness -- _tTotally Bounded Sets -- _tComplete Metric Spaces -- _tFixed Points -- _tCompletions -- _tCompactness -- _tCompact Metric Spaces -- _tUniform Continuity -- _tEquivalent Metrics -- _tCategory -- _tDiscontinuous Functions -- _tBaire Category Theorem -- _tFunction Spaces -- _tSequences of Functions -- _tHistorical Background -- _tPointwise and Uniform Convergence -- _tInterchanging Limits -- _tSpace of Bounded Functions -- _tSpace of Continuous Functions -- _tWeierstrass Theorem -- _tTrigonometric Polynomials -- _tInfinitely Differentiable Functions -- _tEquicontinuity -- _tContinuity and Category -- _tStone-Weierstrass Theorem -- _tAlgebras and Lattices -- _tStone-Weierstrass Theorem -- _tFunctions of Bounded Variation -- _tFunctions of Bounded Variation -- _tHelly's First Theorem -- _tRiemann-Stieltjes Integral -- _tWeights and Measures -- _tRiemann-Stieltjes Integral -- _tSpace of Integrable Functions -- _tIntegrators of Bounded Variation -- _tRiemann Integral -- _tRiesz Representation Theorem -- _tOther Definitions, Other Properties -- _tFourier Series -- _tDirichlet's Formula -- _tFejer's Theorem -- _tComplex Fourier Series -- _tLebesgue Measure and Integration -- _tLebesgue Measure -- _tProblem of Measure -- _tLebesgue Outer Measure -- _tRiemann Integrability -- _tMeasurable Sets -- _tStructure of Measurable Sets -- _tA Nonmeasurable Set -- _tOther Definitions -- _tMeasurable Functions -- _tMeasurable Functions -- _tExtended Real-Valued Functions -- _tSequences of Measurable Functions -- _tApproximation of Measurable Functions -- _tLebesgue Integral -- _tSimple Functions -- _tNonnegative Functions -- _tGeneral Case -- _tLebesgue's Dominated Convergence Theorem -- _tApproximation of Integrable Functions -- _tAdditional Topics -- _tConvergence in Measure -- _tL[subscript p] Spaces -- _tApproximation of L[subscript p] Functions -- _tMore on Fourier Series -- _tDifferentiation -- _tLebesgue's Differentiation Theorem -- _tAbsolute Continuity
520	1		_a"Aimed at advanced undergraduates and beginning graduate students, Real Analysis offers a rigorous yet accessible course in the subject. Carothers, presupposing only a modest background in real analysis or advanced calculus, writes with an informal style and incorporates historical commentary as well as notes and references." "The book looks at metric and linear spaces, offering an introduction to general topology while emphasizing normed linear spaces. It addresses function spaces and provides familiar applications, such as the Weierstrass and Stone-Weierstrass approximation theorems, functions of bounded variation, Riemann-Stieltjes integration, and a brief introduction to Fourier analysis. Finally, it examines Lebesgue measure and integration on the line. Illustrations and abundant exercises round out the text." "Real Analysis will appeal to students in pure and applied mathematics as well as researchers in statistics, education, engineering, and economics."--BOOK JACKET.
530			_a2 _ub
650		0	_aMathematical analysis.
655		1	_aElectronic Books.
856	4	0	_uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=511004&site=eds-live&custid=s3260518 _zClick to access digital title | log in using your CIU ID number and my.ciu.edu password
942			_cOB _D _eEB _hQA _m2000 _QOL _R _x _8NFIC _2LOC
994			_a02 _bNT
999			_c96398 _d96398
902			_a1 _bCynthia Snell _c1 _dCynthia Snell