منابع مشابه
Reduced functions and Jensen measures
Let φ be a locally upper bounded Borel measurable function on a Greenian open set Ω in Rd and, for every x ∈ Ω, let vφ(x) denote the infimum of the integrals of φ with respect to Jensen measures for x on Ω. Twenty years ago, B.J. Cole and T.J. Ransford proved that vφ is the supremum of all subharmonic minorants of φ on X and that the sets {vφ < t}, t ∈ R, are analytic. In this paper, a differen...
متن کاملNearly hyperharmonic functions and Jensen measures
Let (X,H) be a P-harmonic space and assume for simplicity that constants are harmonic. Given a numerical function φ on X which is locally lower bounded, let Jφ(x) := sup{ ∫ ∗ φdμ(x) : μ ∈ Jx(X)}, x ∈ X, where Jx(X) denotes the set of all Jensen measures μ for x, that is, μ is a compactly supported measure on X satisfying ∫ u dμ ≤ u(x) for every hyperharmonic function on X. The main purpose of t...
متن کاملJensen measures without regularity
In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point. In [Co] Cole gave a counterexample to the peak point conjecture by constructing a non-trivial uniform algebra A with co...
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The idea of noncommutative averaging (that is, of a matrix-convex combination of matrixvalued functions) extends quite naturally to the integral of matrix-valued measurable functions with respect to positive matrix-valued measures. In this lecture I will report on collaborative work with F. Zhou, S. Plosker, and M. Kozdron on formulations of some classical integral inequalities (Jensen, Chebysh...
متن کاملInformation Measures via Copula Functions
In applications of differential geometry to problems of parametric inference, the notion of divergence is often used to measure the separation between two parametric densities. Among them, in this paper, we will verify measures such as Kullback-Leibler information, J-divergence, Hellinger distance, -Divergence, … and so on. Properties and results related to distance between probability d...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13688