Les fonctions qui ont la propriété (K) et la mesurabilité des fonctions de deux variables
Less than many translates of a compact nullset may cover the real line
We answer a question of Darji and Keleti by proving that there exists a compact set C₀ ⊂ ℝ of measure zero such that for every perfect set P ⊂ ℝ there exists x ∈ ℝ such that (C₀+x) ∩ P is uncountable. Using this C₀ we answer a question of Gruenhage by showing that it is consistent with ZFC (as it follows e.g. from ) that less than many translates of a compact set of measure zero can cover ℝ.
Levels of concentration between exponential and Gaussian
Lifting and Desintegration
Limites et fonctions d'ensemble
Limites médiales d'après Mokobodzki
Limiting case of the boundedness of fractional integral operators on nonhomogeneous space.
Limits of families of measure algebras
Limits of inverse systems of measures
In this paper the problem of the existence of an inverse (or projective) limit measure of an inverse system of measure spaces is approached by obtaining first a measure on the whole product space .The measure will have many of the properties of a limit measure provided only that the measures possess mild regularity properties.It is shown that can only exist when is itself a “limit” measure in a more general sense, and that must then be the restriction of to the projective limit...
Limsup random fractals.
Lineability and spaceability on vector-measure spaces
It is proved that if X is infinite-dimensional, then there exists an infinite-dimensional space of X-valued measures which have infinite variation on sets of positive Lebesgue measure. In term of spaceability, it is also shown that , the measures with non-σ-finite variation, contains a closed subspace. Other considerations concern the space of vector measures whose range is neither closed nor convex. All of those results extend in some sense theorems of Muñoz Fernández et al. [Linear Algebra Appl....
Linear combinations of Cantor sets
Linear distortion of Hausdorff dimension and Cantor's function.
Let be a mapping from a metric space X to a metric space Y, and let α be a positive real number. Write dim (E) and Hs(E) for the Hausdorff dimension and the s-dimensional Hausdorff measure of a set E. We give sufficient conditions that the equality dim (f(E)) = αdim (E) holds for each E ⊆ X. The problem is studied also for the Cantor ternary function G. It is shown that there is a subset M of the Cantor ternary set such that Hs(M) = 1, with s = log2/log3 and dim(G(E)) = (log3/log2) dim (E), for...
Linear functionals and local measures
Linear operators in the space of regulated functions
Representation of bounded and compact linear operators in the Banach space of regulated functions is given in terms of Perron-Stieltjes integral.
Lipschitz equivalence of graph-directed fractals
This paper studies the geometric structure of graph-directed sets from the point of view of Lipschitz equivalence. It is proved that if and are dust-like graph-directed sets satisfying the transitivity condition, then and are Lipschitz equivalent, and and are quasi-Lipschitz equivalent when they have the same Hausdorff dimension.
Littlewood's inequality for -bimeasures.
Local dimensions of the branching measure on a Galton–Watson tree
Local Lyapunov exponents and a local estimate of Hausdorff dimension
Local monotonicity of Hausdorff measures restricted to curves in
We give a sufficient condition for a curve to ensure that the -dimensional Hausdorff measure restricted to is locally monotone.