Derivation and Integration by Washek F. Pfeffer - 9780521792684

Derivation and IntegrationAuthor(s): Washek F. Pfeffer\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521792684, 978-0521792684\nSynopsis\nThis 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 dimensi.