On the integration of $$L^0$$-Banach $$L^0$$-modules and its applications to vector calculus on $$\textsf{RCD}$$ spaces
On the integration of $$L^0$$-Banach $$L^0$$-modules and its applications to vector calculus on $$\textsf{RCD}$$ spaces
Abstract A finite-dimensional $$\textsf{RCD}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>RCD</mml:mi> </mml:math> space can be foliated into sufficiently regular leaves, where a differential calculus can be performed. Two important examples are given by the measure-theoretic boundary of the superlevel set of a function of bounded variation and the needle decomposition associated to a Lipschitz …