Let μ be a measure on a measure space (X,Λ) with values in Rnandfbe the density of μ with respect to its total variation. We show that the range R(μ)={μ(E):E∈Λ} of μ is strictly convex if and only if the determinant det[f(x1),...,f(xn)] is nonzero a.e. onXn. We apply the result to a class of measures containing those that are generated by Chebyshev systems.
The Vector Measures whose Range is strictly convex / Bianchini, S.; Mariconda, C.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 232:1(1999), pp. 1-19. [10.1006/jmaa.1998.6215]
The Vector Measures whose Range is strictly convex
Bianchini, S.;
1999-01-01
Abstract
Let μ be a measure on a measure space (X,Λ) with values in Rnandfbe the density of μ with respect to its total variation. We show that the range R(μ)={μ(E):E∈Λ} of μ is strictly convex if and only if the determinant det[f(x1),...,f(xn)] is nonzero a.e. onXn. We apply the result to a class of measures containing those that are generated by Chebyshev systems.File in questo prodotto:
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