Derivation and integration /
Pfeffer, Washek F.,
Derivation and integration / Derivation & Integration Washek F. Pfeffer. - Cambridge : Cambridge University Press, 2001. - 1 online resource (xvi, 266 pages) : digital, PDF file(s). - Cambridge tracts in mathematics ; 140 . - Cambridge tracts in mathematics ; 140. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Topology -- Measures -- Covering theorems -- Densities -- Lipschitz maps -- BV functions -- BV sets -- Slices of BV sets -- Approximating BV sets -- Charges -- The definition and examples -- Spaces of charges -- Derivates -- Derivability -- Reduced charges -- Partitions -- Variations of charges -- Some classical concepts -- The essential variation -- The integration problem -- An excursion to Hausdorff measures -- The critical variation -- AC[subscript *] charges -- Essentially clopen sets -- Charges and BV functions -- The charge F x L[superscript 1] -- The space (CH[subscript *](E), S) -- Duality -- More on BV functions -- The charge F [angle] g -- Lipeomorphisms -- Integration -- The R-integral -- Multipliers -- Change of variables -- Averaging -- The Riemann approach -- Charges as distributional derivatives -- The Lebesgue integral -- Extending the integral -- Buczolich's example -- I-convergence -- The GR-integral -- Additional properties.
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.
9780511574764 (ebook)
Integrals, Generalized.
QA312 / .P458 2001
515/.4
Derivation and integration / Derivation & Integration Washek F. Pfeffer. - Cambridge : Cambridge University Press, 2001. - 1 online resource (xvi, 266 pages) : digital, PDF file(s). - Cambridge tracts in mathematics ; 140 . - Cambridge tracts in mathematics ; 140. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Topology -- Measures -- Covering theorems -- Densities -- Lipschitz maps -- BV functions -- BV sets -- Slices of BV sets -- Approximating BV sets -- Charges -- The definition and examples -- Spaces of charges -- Derivates -- Derivability -- Reduced charges -- Partitions -- Variations of charges -- Some classical concepts -- The essential variation -- The integration problem -- An excursion to Hausdorff measures -- The critical variation -- AC[subscript *] charges -- Essentially clopen sets -- Charges and BV functions -- The charge F x L[superscript 1] -- The space (CH[subscript *](E), S) -- Duality -- More on BV functions -- The charge F [angle] g -- Lipeomorphisms -- Integration -- The R-integral -- Multipliers -- Change of variables -- Averaging -- The Riemann approach -- Charges as distributional derivatives -- The Lebesgue integral -- Extending the integral -- Buczolich's example -- I-convergence -- The GR-integral -- Additional properties.
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.
9780511574764 (ebook)
Integrals, Generalized.
QA312 / .P458 2001
515/.4