A charge in the Euclidean space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R Superscript m"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>m</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb {R}^m</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an additive function defined on the family of all bounded BV sets equipped with a suitable topology. We define derivatives of charges and show that each measurable function defined on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R Superscript m"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>m</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb {R}^m</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is equal almost everywhere to the derivative of a charge.
Authors: Eric Howard, Washek F. Pfeffer
DOI: https://doi.org/10.1090/s0002-9939-03-07276-9
Publish Year: 2003
