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Displaying 381 – 400 of 2107

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.

Characterizations of outer measures associated with lattice measures.

Hsu, Pao-Sheng (2000)

International Journal of Mathematics and Mathematical Sciences

Characterizations of snowflake metric spaces.

Tyson, Jeremy T., Wu, Jang-Mei (2005)

Annales Academiae Scientiarum Fennicae. Mathematica

Characterizations of sum form information measures on open domains.

B.R. Ebanks, P.K. Sahoo, P. Kannappan (1997)

Aequationes mathematicae

Characterizing growth and form of fractal cities with allometric scaling exponents.

Chen, Yanguang (2010)

Discrete Dynamics in Nature and Society

Checkerboards, Lipschitz functions and uniform rectifiability.

Peter W. Jones, Nets Hawk Katz, Ana Vargas (1997)

Revista Matemática Iberoamericana

In his recent lecture at the International Congress [S], Stephen Semmes stated the following conjecture for which we provide a proof.Theorem. Suppose Ω is a bounded open set in Rn with n > 2, and suppose that B(0,1) ⊂ Ω, Hn-1(∂Ω) = M < ∞ (depending on n and M) and a Lipschitz graph Γ (with constant L) such that Hn-1(Γ ∩ ∂Ω) ≥ ε.Here Hk denotes k-dimensional Hausdorff measure and B(0,1) the unit ball in Rn. By iterating our proof we obtain a slightly stronger result which allows us...

Choquet integrals in potential theory.

David R. Adams (1998)

Publicacions Matemàtiques

This is a survey of various applications of the notion of the Choquet integral to questions in Potential Theory, i.e. the integral of a function with respect to a non-additive set function on subsets of Euclidean n-space, capacity. The Choquet integral is, in a sense, a nonlinear extension of the standard Lebesgue integral with respect to the linear set function, measure. Applications include an integration principle for potentials, inequalities for maximal functions, stability for solutions to...

Choquet simplexes whose set of extreme points is $K$ -analytic

Michel Talagrand (1985)

Annales de l'institut Fourier

We construct a Choquet simplex $K$ whose set of extreme points $T$ is $𝒦$ -analytic, but is not a $𝒦$ -Borel set. The set $T$ has the surprising property of being a $K_{σ δ}$ set in its Stone-Cech compactification. It is hence an example of a $K_{σ δ}$ set that is not absolute.

Choquetova teorie kapacit

Jaroslav Lukeš, Ivan Netuka, Jiří Veselý (2002)

Pokroky matematiky, fyziky a astronomie

Christensen measurability of polynomial functions and convex functions of higher orders

Zbigniew Gajda (1986)

Annales Polonici Mathematici

Classes of measures which can be embedded in the simple symmetric random walk.

Cox, Alexander M.G., Obloj, Jan K. (2008)

Electronic Journal of Probability [electronic only]

Classical hierarchies form a modern standpoint. Part III. BP-sets

John Burgess, Richard Lockhart (1983)

Fundamenta Mathematicae

Classical hierarchies from a modern standpoint. Part I. C-sets

John Burgess (1983)

Fundamenta Mathematicae

Classical hierarchies from a modern standpoint. Part II. R-sets

John Burgess (1983)

Fundamenta Mathematicae

Classification and extension by the transfinite induction

Michal Šabo (1979)

Mathematica Slovaca

Classification of $s i g m a$ -ideals

Marek Balcerzak (1987)

Mathematica Slovaca

Closed convex hull of set of measurable functions, Riemann-measurable functions and measurability of translations

Michel Talagrand (1982)

Annales de l'institut Fourier

Let $G$ be a locally compact group. Let $L_{t}$ be the left translation in $L^{\infty} (G)$ , given by $L_{t} f (x) = f (t x)$ . We characterize (undre a mild set-theoretical hypothesis) the functions $f \in L^{\infty} (G)$ such that the map $t \to L_{t} f$ from $G$ into $L^{\infty} (G)$ is scalarly measurable (i.e. for $φ \in L^{\infty} (G)^{*}$ , $t \to φ (L_{t} f)$ is measurable). We show that it is the case when $t \to θ (L_{f} t)$ is measurable for each character $θ$ , and if $G$ is compact, if and only if $f$ is Riemann-measurable. We show that $t \to L_{t} f$ is Borel measurable if and only if $f$ is left uniformly continuous.Some of the measure-theoretic tools used there...

Clusters minimizing area plus length of singular curves.

Frank Morgan (1994)

Mathematische Annalen

Coarea integration in metric spaces

Malý, Jan (2003)

Nonlinear Analysis, Function Spaces and Applications

Let $X$ be a metric space with a doubling measure, $Y$ be a boundedly compact metric space and $u : X \to Y$ be a Lebesgue precise mapping whose upper gradient $g$ belongs to the Lorentz space $L_{m, 1}$ , $m \geq 1$ . Let $E \subset X$ be a set of measure zero. Then ${\hat{ℋ}}_{m} (E \cap u^{- 1} (y)) = 0$ for $ℋ_{m}$ -a.e. $y \in Y$ , where $ℋ_{m}$ is the $m$ -dimensional Hausdorff measure and ${\hat{ℋ}}_{m}$ is the $m$ -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of level sets...

Combinatorics on σ-algebras and problem of Banach

Andrzej Pelc (1984)

Fundamenta Mathematicae

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