We establish a decomposition of non-negative Radon measures on which extends that obtained by Strichartz [6] in the setting of -dimensional measures. As consequences, we deduce some well-known properties concerning the density of non-negative Radon measures. Furthermore, some properties of non-negative Radon measures having their Riesz potential in a Lebesgue space are obtained.
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...
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.