000			02766nam a22004575i 4500
001			978-1-4614-7196-7
003			DE-He213
005			20140220082828.0
007			cr nn 008mamaa
008			130430s2013 xxu| s |||| 0|eng d
020			_a9781461471967 _9978-1-4614-7196-7
024	7		_a10.1007/978-1-4614-7196-7 _2doi
050		4	_aQA312-312.5
072		7	_aPBKL _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.42 _223
100	1		_aOvchinnikov, Sergei. _eauthor.
245	1	0	_aMeasure, Integral, Derivative _h[electronic resource] : _bA Course on Lebesgue's Theory / _cby Sergei Ovchinnikov.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2013.
300			_aX, 146 p. 16 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext, _x0172-5939
505	0		_a1 Preliminaries -- 2 Lebesgue Measure -- 3  Lebesgue Integration -- 4 Differentiation and Integration -- A Measure and Integral over Unbounded Sets -- Index.
520			_aThis classroom-tested text is intended for a one-semester course in Lebesgue’s theory.  With over 180 exercises, the text takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students.  The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text.  The presentation is elementary, where σ-algebras are not used in the text on measure theory and Dini’s derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue’s theory are found in the book.
650		0	_aMathematics.
650		0	_aGlobal analysis (Mathematics).
650	1	4	_aMathematics.
650	2	4	_aMeasure and Integration.
650	2	4	_aReal Functions.
650	2	4	_aAnalysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461471950
830		0	_aUniversitext, _x0172-5939
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-7196-7
912			_aZDB-2-SMA
999			_c95868 _d95868