On strengthening the Lebesgue Density Theorem
S. Taylor (1959)
Fundamenta Mathematicae
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S. Taylor (1959)
Fundamenta Mathematicae
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Weiss, Guido (1956)
Portugaliae mathematica
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Lucio R. Berrone (1999)
Revista Matemática Complutense
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Werner Fischer, Ulrich Schöler (1976)
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...
Leonardo Colzani (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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T. Świątkowski (1978)
Fundamenta Mathematicae
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Janusz Dronka (1993)
Collectanea Mathematica
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In this paper we give estimations of Istratescu measure of noncompactness I(X) of a set X C lp(E1,...,En) in terms of measures I(Xj) (j=1,...,n) of projections Xj of X on Ej. Also a converse problem of finding a set X for which the measure I(X) satisfies the estimations under consideration is considered.
Thomas William Körner (1996)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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