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Displaying 401 – 420 of 2299

Characters and inner forms of a quasi-split group over $R$

D. Shelstad (1979)

Compositio Mathematica

Charakterisierung stetiger Faltungshalbgruppen durch das Lévy-Maß.

Arnold Janssen (1979)

Mathematische Annalen

Chu-Dualität und zwei Klassen maximal fastperiodischer Gruppen.

Detlev Poguntke (1976)

Monatshefte für Mathematik

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...

Closed ideals in certain Beurling algebras, and synthesis of hyperdistributions

J. Esterle (1996)

Studia Mathematica

Closed Ideals in Subalgebras of Banach Algebras II: Ditkin's Condition.

J.T. Burnham (1974)

Monatshefte für Mathematik

Closed Ideals of Homogeneous Algebras.

J.A. Ward (1983)

Monatshefte für Mathematik

Closed subgroups of nuclear spaces are weakly closed

Wojciech Banaszczyk (1984)

Studia Mathematica

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...