Radon-Nikodym property for vector-valued integrable functions
It is proved that if a Frechet space has property, then also has property, for .
Surjit Singh Khurana (1978)
Annales de l'institut Fourier
It is proved that if a Frechet space has property, then also has property, for .
Jirí Navrátil (1981)
Mathematica Scandinavica
H. Sarbadhikari, S. Sirvastava (1990)
Fundamenta Mathematicae
Ryotaro Sato (1980)
Studia Mathematica
M. Wilhelm (1975)
Colloquium Mathematicae
Zdena Riečanová (1984)
Mathematica Slovaca
Diego Averna (1994)
Mathematica Slovaca
Andrzej Kisielewicz (1996)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has . Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.
Ivan Dobrakov (1986)
Mathematica Slovaca
Andrzej Kasperski (2011)
Banach Center Publications
In this paper we consider some spaces of differentiable multifunctions, in particular the generalized Orlicz-Sobolev spaces of multifunctions, we study completeness of them, and give some theorems.
Gogodze, Ioseb K., Gelashvili, Koba N. (1997)
Memoirs on Differential Equations and Mathematical Physics
Ivan Dobrakov (1989)
Czechoslovak Mathematical Journal
Fabio Berra (2022)
Czechoslovak Mathematical Journal
We give a quantitative characterization of the pairs of weights for which the dyadic version of the one-sided Hardy-Littlewood maximal operator satisfies a restricted weak type inequality for . More precisely, given any measurable set , the estimate holds if and only if the pair belongs to , that is, for every dyadic cube and every measurable set . The proof follows some ideas appearing in S. Ombrosi (2005). We also obtain a similar quantitative characterization for the non-dyadic...
A. Sikorska-Nowak (2007)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
We prove an existence theorem for the equation x' = f(t,xₜ), x(Θ) = φ(Θ), where xₜ(Θ) = x(t+Θ), for -r ≤ Θ < 0, t ∈ Iₐ, Iₐ = [0,a], a ∈ R₊ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness.
Dragomir, S.S. (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Valeria Marraffa (2006)
Czechoslovak Mathematical Journal
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Werner Rupp (1979)
Mathematische Annalen
Umi Mahnuna Hanung (2024)
Mathematica Bohemica
In the theories of integration and of ordinary differential and integral equations, convergence theorems provide one of the most widely used tools. Since the values of the Kurzweil-Stieltjes integrals over various kinds of bounded intervals having the same infimum and supremum need not coincide, the Harnack extension principle in the Kurzweil-Henstock integral, which is a key step to supply convergence theorems, cannot be easily extended to the Kurzweil-type Stieltjes integrals with discontinuous...
Anna Kucia (1991)
Fundamenta Mathematicae
Henry Helson (1979)
Bulletin de la Société Mathématique de France