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007			cr |uu|||uu|||
008			190107s2017 si a ob 001 0 eng d
010			_z 2015029065 _z 2016013681
040			_aWSPC _beng _cWSPC
020			_a9789813221673 _q(ebook)
020			_z9789813221598 _q(hbk.)
020			_z9789813221635 _q(pbk.)
050	0	4	_aQA300 _b.J27 2017 v. 3
072		7	_aMAT _x007000 _2bisacsh
072		7	_aMAT _x034000 _2bisacsh
072		7	_aMAT _x040000 _2bisacsh
082	0	4	_a515 _223
100	1		_aJacob, Niels. _920859
245	1	2	_aA course in analysis. _nV. III, _pMeasure and integration theory, complex-valued functions of a complex variable _h[electronic resource] / _cNiels Jacob, Kristian P. Evans.
246	3	0	_aMeasure and integration theory, complex-valued functions of a complex variable
260			_aSingapore : _bWorld Scientific Publishing Co. Pte Ltd., _c©2017.
300			_a1 online resource (784 p.) : _bill.
538			_aSystem requirements: Adobe Acrobat Reader.
538			_aMode of access: World Wide Web.
588			_aTitle from web page (viewed January 17, 2019).
504			_aIncludes bibliographical references and index.
520			_a"In this third volume of "A Course in Analysis", two topics indispensible for every mathematician are treated: Measure and Integration Theory; and Complex Function Theory. In the first part measurable spaces and measure spaces are introduced and Caratheodory's extension theorem is proved. This is followed by the construction of the integral with respect to a measure, in particular with respect to the Lebesgue measure in the Euclidean space. The Radon-Nikodym theorem and the transformation theorem are discussed and much care is taken to handle convergence theorems with applications, as well as Lp-spaces. Integration on product spaces and Fubini's theorem is a further topic as is the discussion of the relation between the Lebesgue integral and the Riemann integral. In addition to these standard topics we deal with the Hausdorff measure, convolutions of functions and measures including the Friedrichs mollifier, absolutely continuous functions and functions of bounded variation. The fundamental theorem of calculus is revisited, and we also look at Sard's theorem or the Riesz-Kolmogorov theorem on pre-compact sets in Lp-spaces. The text can serve as a companion to lectures, but it can also be used for self-studying. This volume includes more than 275 problems solved completely in detail which should help the student further."-- _cPublisher's website.
650		0	_aMathematical analysis _vTextbooks. _912177
650		0	_aMathematics _xStudy and teaching (Higher) _920860
650		0	_aCalculus _vTextbooks. _921051
650		0	_aElectronic books. _921052
700	1		_aEvans, Kristian P. _920863
856	4	0	_uhttps://www.worldscientific.com/worldscibooks/10.1142/10548#t=toc _zAccess to full text is restricted to subscribers.
942			_cEBK
999			_c72714 _d72714