000			03241nam a22003738i 4500
001			CR9780511574764
003			UkCbUP
005			20200124160235.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090522s2001||||enk o ||1 0|eng|d
020			_a9780511574764 (ebook)
020			_z9780521792684 (hardback)
020			_z9780521155656 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA312 _b.P458 2001
082	0	0	_a515/.4 _221
100	1		_aPfeffer, Washek F., _eauthor.
245	1	0	_aDerivation and integration / _cWashek F. Pfeffer.
246	3		_aDerivation & Integration
264		1	_aCambridge : _bCambridge University Press, _c2001.
300			_a1 online resource (xvi, 266 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v140
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tTopology -- _tMeasures -- _tCovering theorems -- _tDensities -- _tLipschitz maps -- _tBV functions -- _tBV sets -- _tSlices of BV sets -- _tApproximating BV sets -- _tCharges -- _tThe definition and examples -- _tSpaces of charges -- _tDerivates -- _tDerivability -- _tReduced charges -- _tPartitions -- _tVariations of charges -- _tSome classical concepts -- _tThe essential variation -- _tThe integration problem -- _tAn excursion to Hausdorff measures -- _tThe critical variation -- _tAC[subscript *] charges -- _tEssentially clopen sets -- _tCharges and BV functions -- _tThe charge F x L[superscript 1] -- _tThe space (CH[subscript *](E), S) -- _tDuality -- _tMore on BV functions -- _tThe charge F [angle] g -- _tLipeomorphisms -- _tIntegration -- _tThe R-integral -- _tMultipliers -- _tChange of variables -- _tAveraging -- _tThe Riemann approach -- _tCharges as distributional derivatives -- _tThe Lebesgue integral -- _tExtending the integral -- _tBuczolich's example -- _tI-convergence -- _tThe GR-integral -- _tAdditional properties.
520			_aThis 2001 book is devoted to an invariant multidimensional process of recovering a function from its derivative. It considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. A typical example is the flux of a continuous vector field. A very general Gauss-Green theorem follows from the sufficient conditions for the derivability of the flux. Since the setting is invariant with respect to local lipeomorphisms, a standard argument extends the Gauss-Green theorem to the Stokes theorem on Lipschitz manifolds. In addition, the author proves the Stokes theorem for a class of top-dimensional normal currents - a first step towards solving a difficult open problem of derivation and integration in middle dimensions. The book contains complete and detailed proofs and will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas.
650		0	_aIntegrals, Generalized.
776	0	8	_iPrint version: _z9780521792684
830		0	_aCambridge tracts in mathematics ; _v140.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511574764
999			_c517984 _d517982