000			05015cam a2200697Ma 4500
001			ocn892046052
003			OCoLC
005			20171026104637.0
006			m o d
007			cr |n|||||||||
008			141003s2014 enk ob 001 0 eng d
020			_a9781119037514 _q(electronic bk.)
020			_a1119037514 _q(electronic bk.)
020			_a1322150052 _q(ebk)
020			_a9781322150055 _q(ebk)
020			_a9781119037385
020			_a1119037387
020			_a1848217692
020			_a9781848217690
020			_z9781848217690
029	1		_aCHBIS _b010259839
029	1		_aCHVBK _b325940541
029	1		_aDEBBG _bBV042990065
029	1		_aDEBBG _bBV043397180
029	1		_aDEBSZ _b431774137
035			_a(OCoLC)892046052 _z(OCoLC)892800065 _z(OCoLC)961535390 _z(OCoLC)962610842
037			_a646260 _bMIL
040			_aIDEBK _beng _epn _cIDEBK _dDG1 _dE7B _dOCLCA _dRECBK _dCDX _dEBLCP _dN$T _dYDXCP _dOCLCQ _dVRC _dOCLCF _dDEBSZ _dCOO _dOCLCO _dOCLCQ _dDEBBG _dOCLCQ
049			_aMAIN
050		4	_aQA312 _b.M33 2014
072		7	_aMAT _x005000 _2bisacsh
072		7	_aMAT _x034000 _2bisacsh
082	0	4	_a515/.42 _223
100	1		_aMackevičius, Vigirdas.
245	1	0	_aIntegral and measure : from rather simple to rather complex / _cVigirdas Mackevičius. _h[electronic resource]
260			_aLondon : _bISTE, Ltd ; _aHoboken : _bWiley, _c2014.
300			_a1 online resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMathematics and Statistics Series
504			_aIncludes bibliographical references and index.
505	0		_aCover page; Half-title page; Title page; Copyright page; Contents; Preface; Note for the Teacher or Who is better, Riemann or Lebesgue?; Notation; Part 1: Integration of One-Variable Functions; 1: Functions without Second-kind Discontinuities; P.1. Problems; 2: Indefinite Integral; P.2. Problems; 3: Definite Integral; 3.1. Introduction; P.3. Problems; 4: Applications of the Integral; 4.1. Area of a curvilinear trapezium; 4.2. A general scheme for applying the integrals; 4.3. Area of a surface of revolution; 4.4. Area of curvilinear sector; 4.5. Applications in mechanics; P.4. Problems.
505	8		_a5: Other Definitions: Riemann and Stieltjes Integrals5.1. Introduction; P.5. Problems; 6: Improper Integrals; P.6. Problems; Part 2: Integration of Several-variable Functions; 7: Additional Properties of Step Functions; 7.1. The notion "almost everywhere"; P.7. Problems; 8: Lebesgue Integral; 8.1. Proof of the correctness of the definition of integral; 8.2. Proof of the Beppo Levi theorem; 8.3. Proof of the Fatou-Lebesgue theorem; P.8. Problems; 9: Fubini and Change-of-Variables Theorems; P.9. Problems; 10: Applications of Multiple Integrals; 10.1. Calculation of the area of a plane figure.
505	8		_a10.2. Calculation of the volume of a solid10.3. Calculation of the area of a surface; 10.4. Calculation of the mass of a body; 10.5. The static moment and mass center of a body; 11: Parameter-dependent Integrals; 11.1. Introduction; 11.2. Improper PDIs; P.11. Problems; Part 3: Measure and Integration in a Measure Space; 12: Families of Sets; 12.1. Introduction; P.12. Problems; 13: Measure Spaces; P.13. Problems; 14: Extension of Measure; P.14. Problems; 15: Lebesgue-Stieltjes Measures on the Real Line and Distribution Functions; P.15 Problems.
505	8		_a16: Measurable Mappings and Real Measurable FunctionsP. 16. Problems; 17: Convergence Almost Everywhere and Convergence in Measure; P.17. Problems; 18: Integral; P.18. Problems; 19: Product of Two Measure Spaces; P.19. Problems; Bibliography; Index.
520			_aThis book is devoted to integration, one of the two main operations in calculus. In Part 1, the definition of the integral of a one-variable function is different (not essentially, but rather methodically) from traditional definitions of Riemann or Lebesgue integrals. Such an approach allows us, on the one hand, to quickly develop the practical skills of integration as well as, on the other hand, in Part 2, to pass naturally to the more general Lebesgue integral. Based on the latter, in Part 2, the author develops a theory of integration for functions of several variables. In Part 3, within.
588	0		_aPrint version record.
650		0	_aIntegrals, Generalized.
650		4	_aLebesgue integral.
650		4	_aMathematics.
650		4	_aMeasurement.
650		7	_aMATHEMATICS _xCalculus. _2bisacsh
650		7	_aMATHEMATICS _xMathematical Analysis. _2bisacsh
650		7	_aIntegrals, Generalized. _2fast _0(OCoLC)fst00975523
655		4	_aElectronic books.
776	0	8	_iPrint version: _aMackevicius, Vigirdas. _tIntegral and measure. _dLondon : Iste Ltd, 2014 _z1848217692 _w(OCoLC)891671114
830		0	_aOregon State monographs. _pMathematics and statistics series.
856	4	0	_uhttp://onlinelibrary.wiley.com/book/10.1002/9781119037514 _zWiley Online Library
942			_2ddc _cBK
999			_c207699 _d207699