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• catalog abstract ""This 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 toward solving a difficult open problem of derivation and integration in middle dimensions." "The book contains complete and detailed proofs of all new results, and of many known results for which the references are not easily available. It will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas."--Jacket.".
• catalog contributor b12113058.
• catalog created "c2001.".
• catalog date "2001".
• catalog date "c2001.".
• catalog dateCopyrighted "c2001.".
• catalog description ""This 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 toward solving a difficult open problem of derivation and integration in middle dimensions." "The book contains complete and detailed proofs of all new results, and of many known results for which the references are not easily available. It will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas."--Jacket.".
• catalog description "Includes bibliographical references (p. 255-258) and index.".
• catalog description "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.".
• catalog extent "xvi, 266 p. ;".
• catalog identifier "0521792681".
• catalog isPartOf "Cambridge tracts in mathematics ; 140".
• catalog issued "2001".
• catalog issued "c2001.".
• catalog language "eng".
• catalog publisher "Cambridge, UK ; New York : Cambridge University Press,".
• catalog subject "515/.4 21".
• catalog subject "Integrals, Generalized.".
• catalog subject "QA312 .P458 2001".
• catalog tableOfContents "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.".
• catalog title "Derivation and integration / Washek F. Pfeffer.".
• catalog type "text".