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 Differentiation Theorem for Additive Processes.
A dimension group for local homeomorphisms and endomorphisms of onesided shifts fo finite type.
A discrete version of an open problem and several answers.
A dominated convergence theorem for real-valued summable set functions
A dominated ergodic estimate for spaces with weights
A dynamical interpretation of the global canonical height on an elliptic curve.
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 Ford-Fulkerson type theorem concerning vector-valued flows in infinite networks
A Formula for Popp’s Volume in Sub-Riemannian Geometry
For an equiregular sub-Riemannian manifold M, Popp’s volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp’s volume, written in terms of a frame adapted to the sub-Riemannian distribution. As a first application of this result, we prove an explicit formula for the canonical sub- Laplacian, namely the one associated with Popp’s volume. Finally, we discuss...
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 Function with Countably Many Ergodic Equilibrium States.
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 approach to decomposable bi-capacities
We propose a concept of decomposable bi-capacities based on an analogous property of decomposable capacities, namely the valuation property. We will show that our approach extends the already existing concepts of decomposable bi-capacities. We briefly discuss additive and -additive bi-capacities based on our definition of decomposability. Finally we provide examples of decomposable bi-capacities in our sense in order to show how they can be constructed.
A general bounded continuous moment problem and its sets of uniqueness
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.