Orlicz spaces based on families of measures
Robert Rosenberg (1970)
Studia Mathematica
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Robert Rosenberg (1970)
Studia Mathematica
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Janusz Matkowski (1994)
Studia Mathematica
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Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then...
M. Laczkovich, G. Petruska (1978)
Fundamenta Mathematicae
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Cristian E. Gutiérrez, Annamaria Montanari (2004)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In the euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous –convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives...
R. Ger (1970)
Fundamenta Mathematicae
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Françoise Lust-Piquard, Walter Schachermayer (1989)
Studia Mathematica
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Ivanov, M., Zlateva, N. (2000)
Serdica Mathematical Journal
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We consider the question whether the assumption of convexity of the set involved in Clarke-Ledyaev inequality can be relaxed. In the case when the point is outside the convex hull of the set we show that Clarke-Ledyaev type inequality holds if and only if there is certain geometrical relation between the point and the set.
Lynn Williams, J. Wells, T. Hayden (1971)
Studia Mathematica
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Zoltán Daróczy, Zsolt Páles (1987)
Stochastica
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