000			04161cam a2200409Mi 4500
001			on1250259089
003			OCoLC
005			20240726104837.0
008			210510s2021 xx o 0|| 0 eng d
040			_aYDX _beng _erda _cYDX _dNT _dEBLCP _dUKAHL
020			_a9781536196177 _q((electronic)l(electronic)ctronic)
050	0	4	_aQA431 _b.I584 2021
049			_aMAIN
100	1		_aXIAO, JIE. _e1
245	1	0	_aINTEGRAL AND FUNCTIONAL ANALYSIS (UPDATED EDITION)
300			_a1 online resource
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_adata file _2rda
490	1		_aMathematics Research Developments Ser.
504			_a2
505	0	0	_aIntro -- _tINTEGRAL AND FUNCTIONALANALYSIS(UPDATED EDITION) -- _tINTEGRAL AND FUNCTIONALANALYSIS(UPDATED EDITION) -- _tContents -- _tPreface -- _tAcknowledgments -- _tChapter 1Preliminaries -- _t1.1 Sets, Relations, Functions, Cardinals and Ordinals -- _t1.2 Reals, Some Basic Theorems and Sequence Limits -- _tProblems -- _tChapter 2Riemann Integrals -- _t2.1 Definitions, Examples and Basic Properties -- _t2.2 Algebraic Operations and the Darboux Criterion -- _t2.3 Fundamental Theorem of Calculus -- _t2.4 Improper Integrals -- _tProblems -- _tChapter 3Riemann-Stieltjes Integrals -- _t3.1 Functions of Bounded Variation
505	0	0	_a3.2 Definition and Basic Properties -- _t3.3 Nonexistence and Existence for Integrals -- _t3.4 Evaluations of Integrals -- _t3.5 Improper Situations -- _tProblems -- _tChapter 4Lebesgue-Radon-StieltjesIntegrals -- _t4.1 Foundational Material -- _t4.2 Essential Properties -- _t4.3 Convergence Theorems -- _t4.4 Extension via Measurability -- _t4.5 Double, Iterated and Generic Integrals -- _tProblems -- _tChapter 5Absolute Continuitiesin Lebesgue Integrals -- _t5.1 Lebesgue's Outer Measure and Vitali's Covering -- _t5.2 Derivatives of Increasing Functions -- _t5.3 Absolutely Continuous Functions
505	0	0	_a5.4 Cantor's Ternary Set and Singular Function -- _t5.5 Lebesgue's Points -- _tProblems -- _tChapter 6Metric Spaces -- _t6.1 Metrizable Topology and Connectedness -- _t6.2 Completeness -- _t6.3 Compactness, Density and Separability -- _tProblems -- _tChapter 7Continuous Mappings -- _t7.1 Criteria for Continuity -- _t7.2 Continuous Mappings over Compactor ConnectedMetric Spaces -- _t7.3 Sequences of Mappings -- _t7.4 Contractions -- _t7.5 Structures of Metric Spaces -- _tProblems -- _tChapter 8Normed Linear Spaces -- _t8.1 Linear Spaces, Norms and Quotient Spaces -- _t8.2 Finite Dimensional Spaces -- _t8.3 Bounded Linear Operators
505	0	0	_a8.4 Linear Functionals via Hahn-Banach Extension -- _tProblems -- _tChapter 9Banach Spaces via Operatorsand Functionals -- _t9.1 Definition and Beginning Examples -- _t9.2 Uniform Boundedness -- _tOpen Map -- _tClosed Graph -- _t9.3 Dual Banach Spaces by Examples -- _t9.4 Weak and Weak* Topologies -- _t9.5 Compact and Dual Operators -- _tProblems -- _tChapter 10Hilbert Spaces and TheirOperators -- _t10.1 Definition, Examples and Basic Properties -- _t10.2 Orthogonality, Orthogonal Complementand Duality -- _t10.3 Orthonormal Sets and Bases -- _t10.4 Five Special Bounded Operators -- _t10.5 Compact Operators via Spectrum -- _tProblems
505	0	0	_aHints or Solutions -- _t1 Preliminaries -- _t3 Riemann-Stieltjes Integrals -- _t4 Lebesgue-Radon-Stieltjes Integrals -- _t5 Absolute Continuities in Lebesgue Integrals -- _t6 Metric Spaces -- _t7 Continuous Mappings -- _t8 Normed Linear Spaces -- _t9 Banach Spaces via Operators and Functionals -- _t10 Hilbert Spaces and Their Operators -- _t2 Riemann Integrals -- _tReferences -- _tAbout the Author -- _tIndex -- _tBlank Page -- _tBlank Page
530			_a2 _ub
650		0	_aIntegral equations.
650		0	_aMetric spaces.
650		0	_aFunctional analysis.
655		1	_aElectronic Books.
856	4	0	_zClick to access digital title | log in using your CIU ID number and my.ciu.edu password. _uhttpss://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=2913944&site=eds-live&custid=s3260518
942			_cOB _D _eEB _hQA _m2021 _QOL _R _x _8NFIC _2LOC
994			_a92 _bNT
999			_c80220 _d80220
902			_a1 _bCynthia Snell _c1 _dCynthia Snell