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Central limit theorems for non-invertible measure preserving maps

Michael C. Mackey, Marta Tyran-Kamińska (2008)

Colloquium Mathematicae

Using the Perron-Frobenius operator we establish a new functional central limit theorem for non-invertible measure preserving maps that are not necessarily ergodic. We apply the result to asymptotically periodic transformations and give a specific example using the tent map.

Chaotic behavior of infinitely divisible processes

S. Cambanis, K. Podgórski, A. Weron (1995)

Studia Mathematica

The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.

Characteristic points, rectifiability and perimeter measure on stratified groups

Valentino Magnani (2006)

Journal of the European Mathematical Society

We establish an explicit connection between the perimeter measure of an open set E with C 1 boundary and the spherical Hausdorff measure S Q − 1 restricted to ∂ E , when the ambient space is a stratified group endowed with a left invariant sub-Riemannian metric and Q denotes the Hausdorff dimension of the group. Our formula implies that the perimeter measure of E is less than or equal to S Q − 1 ( ∂ E ) up to a dimensional factor. The validity of this estimate positively answers a conjecture raised by Danielli, Garofalo...

Characterization of local dimension functions of subsets of ℝ d

L. Olsen (2005)

Colloquium Mathematicae

For a subset E ⊆ ℝ d and x ∈ ℝ d , the local Hausdorff dimension function of E at x is defined by d i m H , l o c ( x , E ) = l i m r ↘ 0 d i m H ( E ∩ B ( x , r ) ) where d i m H denotes the Hausdorff dimension. We give a complete characterization of the set of functions that are local Hausdorff dimension functions. In fact, we prove a significantly more general result, namely, we give a complete characterization of those functions that are local dimension functions of an arbitrary regular dimension index.

Characterization of optimal shapes and masses through Monge-Kantorovich equation

Guy Bouchitté, Giuseppe Buttazzo (2001)

Journal of the European Mathematical Society

We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.

Characterization of Strongly Exposed Points in General Köthe-Bochner Banach Spaces

Houcine Benabdellah, My Hachem Lalaoui Rhali (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We study strongly exposed points in general Köthe-Bochner Banach spaces X(E). We first give a characterization of strongly exposed points of the set of X-selections of a measurable multifunction Γ. We then apply this result to the study of strongly exposed points of the closed unit ball of X(E). Precisely we show that if an element f is a strongly exposed point of B X ( E ) , then |f| is a strongly exposed point of B X and f(ω)/∥ f(ω)∥ is a strongly exposed point of B E for μ-almost all ω ∈ S(f).

Characterization of σ-porosity via an infinite game

Martin Doležal (2012)

Fundamenta Mathematicae

Let X be an arbitrary metric space and P be a porosity-like relation on X. We describe an infinite game which gives a characterization of σ-P-porous sets in X. This characterization can be applied to ordinary porosity above all but also to many other variants of porosity.

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