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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… Click to show full abstract
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.
Keywords:
vector measures;
convergence;
monotonicity;
range convergence;
range
Journal Title: Ricerche di Matematica
Year Published: 2019
Link to full text (if available)
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Journal Title: Ricerche di Matematica
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!