A Dieudonné theorem for lattice group-valued measures
A version of Dieudonné theorem is proved for lattice group-valued modular measures on lattice ordered effect algebras. In this way we generalize some results proved in the real-valued case.
A discrete version of an open problem and several answers.
A dominated convergence theorem for real-valued summable set functions
A family of singular functions and its relation to harmonic fractal analysis and fuzzy logic
We study a parameterized family of singular functions which appears in a paper by H. Okamoto and M. Wunsch (2007). Various properties are revisited from the viewpoint of fractal geometry and probabilistic techniques. Hausdorff dimensions are calculated for several sets related to these functions, and new properties close to fractal analysis and strong negations are explored.
A Fourier analytical characterization of the Hausdorff dimension of a closed set and of related Lebesgue spaces
Let Γ be a closed set in with Lebesgue measure |Γ| = 0. The first aim of the paper is to give a Fourier analytical characterization of Hausdorff dimension of Γ. Let 0 < d < n. If there exist a Borel measure µ with supp µ ⊂ Γ and constants and such that for all 0 < r < 1 and all x ∈ Γ, where B(x,r) is a ball with centre x and radius r, then Γ is called a d-set. The second aim of the paper is to provide a link between the related Lebesgue spaces , 0 < p ≤ ∞, with respect to...
A Fubini-type theorem for finitely additive measure spaces
A further investigation for Egoroff's theorem with respect to monotone set functions
In this paper, we investigate Egoroff’s theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff’s theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff’s theorem for non-additive measure is formulated in full generality.
A game of fair division with continuum of players
A general form of the Vitali theorem
A general purity law for convolution semigroups with discrete Levy measure.
A general rearrangement inequality à la Hardy-Littlewood.
A general result on the equivalence between derivation of integrals and weak inequalities for the Hardy-Littlewood maximal operator
A generalised conical density theorem for unrectifiable sets.
A Generalization Of Fubini's Theorem For Banach Algebra-Valued Measures.
A generalization of Rademacher's theorem on complete differential
A generalization of Steinhaus' theorem to coordinatewise measure preserving binary transformations
A generalization of the Lagrange mean value theorem to the case of vector-valued mappings.
A generalization of the Nikodym boundedness theorem.
In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.
A generalization of the Vitali covering theorem
A generalization of Yano's extrapolation theorem