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Derivation and integration

Pfeffer, Washek F.

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Derivation and integration

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Derivation and integration/ Washek F. Pfeffer.
其他題名:	Derivation & Integration
作者:	Pfeffer, Washek F.
出版者:	Cambridge :Cambridge University Press, : 2001.,
面頁冊數:	xvi, 266 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Integrals, Generalized. -
電子資源:	https://doi.org/10.1017/CBO9780511574764
ISBN:	9780511574764

Derivation and integration
Pfeffer, Washek F.

Derivation and integration[electronic resource] /Derivation & IntegrationWashek F. Pfeffer. - Cambridge :Cambridge University Press,2001. - xvi, 266 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;140. - Cambridge tracts in mathematics ;140..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Topology --

This 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.

ISBN: 9780511574764Subjects--Topical Terms:

544186
Integrals, Generalized.

LC Class. No.: QA312 / .P458 2001

Dewey Class. No.: 515.4

Derivation and integration
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246 3 $a Derivation & Integration
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300 $a xvi, 266 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 140
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $t Topology -- $t Measures -- $t Covering theorems -- $t Densities -- $t Lipschitz maps -- $t BV functions -- $t BV sets -- $t Slices of BV sets -- $t Approximating BV sets -- $t Charges -- $t The definition and examples -- $t Spaces of charges -- $t Derivates -- $t Derivability -- $t Reduced charges -- $t Partitions -- $t Variations of charges -- $t Some classical concepts -- $t The essential variation -- $t The integration problem -- $t An excursion to Hausdorff measures -- $t The critical variation -- $t AC[subscript *] charges -- $t Essentially clopen sets -- $t Charges and BV functions -- $t The charge F x L[superscript 1] -- $t The space (CH[subscript *](E), S) -- $t Duality -- $t More on BV functions -- $t The charge F [angle] g -- $t Lipeomorphisms -- $t Integration -- $t The R-integral -- $t Multipliers -- $t Change of variables -- $t Averaging -- $t The Riemann approach -- $t Charges as distributional derivatives -- $t The Lebesgue integral -- $t Extending the integral -- $t Buczolich's example -- $t I-convergence -- $t The GR-integral -- $t Additional properties.
520 $a This 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 $a Integrals, Generalized. $3 544186
830 0 $a Cambridge tracts in mathematics ; $v 140. $3 3470691
856 4 0 $u https://doi.org/10.1017/CBO9780511574764