On a set in under coordinate transformations
On a Sobolev type inequality and its applications
Assume ||·|| is a norm on ℝⁿ and ||·||⁎ its dual. Consider the closed ball , r > 0. Suppose φ is an Orlicz function and ψ its conjugate. We prove that for arbitrary A,B > 0 and for each Lipschitz function f on T, , where |·| is the Lebesgue measure on ℝⁿ. This is a strengthening of the Sobolev inequality obtained by M. Talagrand. We use this inequality to state, for a given concave, strictly increasing function η: ℝ₊ → ℝ with η(0) = 0, a necessary and sufficient condition on φ so that each...
On a sum of observables in a logic
On a summability of observables in generalized measurable spaces
On a theorem concerning uniform integrability.
On a theorem of Beardon and Maskit.
On a Theorem of Gersgorin.
On a theorem of Holický and Zelený concerning Borel maps without -compact fibers
The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.
On a theorem of S. Banach.
On absolutely measurable sets
On abstract Stieltjes measure
In 1955, A. Revuz - Annales de l’Institut Fourier, vol. 6 (1955-56) - considered a type of Stieltjes measure defined on analogues of half-open, half-closed intervals in a partially ordered topological space. He states that these functions are finitely additive but his proof has an error. We shall furnish a new proof and extend some of this results to “measures” taking values in a topological abelian group.
On a.e. convergence of expansion with respect to a bounded orthonormal system of polygonals
On Alexandrov lattices.
On almost invariant subsets of the real line
On an Abstract Formulation of Absolute Continuity and Dominancy
On an Abstract Formulation of Regularity
On an application of hypoellipticity to solutions of functional equations.
On an exponential inequality and a strong law of large numbers for monotone measures
An exponential inequality for Choquet expectation is discussed. We also obtain a strong law of large numbers based on Choquet expectation. The main results of this paper improve some previous results obtained by many researchers.
On an Extendability Problem for Measures.
On an extension of finite functionals by the transfinite induction