Range convergence monotonicity for vector measures and range monotonicity of the mass

11 Apr 2019  ·  Dekeyser Justin, Van Schaftingen Jean ·

We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the strict convergence implies the range convergence for strictly convex norms. In dimension 2 and for Euclidean spaces of any dimensions, we prove that the total variation of a vector measure is monotone with respect to the range...

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Classical Analysis and ODEs Functional Analysis