On ultra-weak convergence in $L^p$

Donald E. Myers

Displaying similar documents to “On ultra-weak convergence in $L^{p}$ ”

Convergence in the dual of certain $K M_{p}$ -spaces

Larry Kitchens, Charles Swartz (1974)

Colloquium Mathematicae

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Convergence of greedy approximation I. General systems

S. V. Konyagin, V. N. Temlyakov (2003)

Studia Mathematica

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We consider convergence of thresholding type approximations with regard to general complete minimal systems eₙ in a quasi-Banach space X. Thresholding approximations are defined as follows. Let eₙ* ⊂ X* be the conjugate (dual) system to eₙ; then define for ε > 0 and x ∈ X the thresholding approximations as $T_{ε} (x) : = \sum_{j \in D_{ε} (x)} e *_{j} (x) e_{j}$ , where $D_{ε} (x) : = j : | e *_{j} (x) | \geq ε$ . We study a generalized version of $T_{ε}$ that we call the weak thresholding approximation. We modify the $T_{ε} (x)$ in the following way. For ε > 0, t ∈ (0,1) we set $D_{t, ε} (x) : = j : t ε \leq | e *_{j} (x) | < ε$ and consider...

On the completeness of $ℒ_{p}$ -spaces over a charge

Sreela Gangopadhyay (1990)

Colloquium Mathematicae

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The subspace of weak $P$ -points of $ℕ^{*}$

Salvador García-Ferreira, Y. F. Ortiz-Castillo (2015)

Commentationes Mathematicae Universitatis Carolinae

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Let $W$ be the subspace of $ℕ^{*}$ consisting of all weak $P$ -points. It is not hard to see that $W$ is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that $W$ is a $p$ -pseudocompact space for all $p \in ℕ^{*}$ .

Weak convergence of mutually independent $X ₙ^{B}$ and $X ₙ^{A}$ under weak convergence of $X ₙ \equiv X ₙ^{B} - X ₙ^{A}$

W. Szczotka (2006)

Applicationes Mathematicae

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For each n ≥ 1, let $v_{n, k}, k \geq 1$ and $u_{n, k}, k \geq 1$ be mutually independent sequences of nonnegative random variables and let each of them consist of mutually independent and identically distributed random variables with means v̅ₙ and u̅̅ₙ, respectively. Let $X ₙ^{B} (t) = (1 / c ₙ) \sum_{j = 1}^{[n t]} (v_{n, j} - v ̅ ₙ)$ , $X ₙ^{A} (t) = (1 / c ₙ) \sum_{j = 1}^{[n t]} (u_{n, j} - u ̅ ̅ ₙ)$ , t ≥ 0, and $X ₙ = X ₙ^{B} - X ₙ^{A}$ . The main result gives conditions under which the weak convergence $X ₙ \overset{}{\to} X$ , where X is a Lévy process, implies $X ₙ^{B} \overset{}{\to} X^{B}$ and $X ₙ^{A} \overset{}{\to} X^{A}$ , where $X^{B}$ and $X^{A}$ are mutually independent Lévy processes and $X = X^{B} - X^{A}$ .

Compactness in $C_{s} (T)$ and Applications

Richard Haydon (1972)

Publications du Département de mathématiques (Lyon)

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The weak convergence of regenerative processes using some excursion path decompositions

Amaury Lambert, Florian Simatos (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We consider regenerative processes with values in some general Polish space. We define their $ε$ -big excursions as excursions $e$ such that $ϕ (e) g t; ε$ , where $ϕ$ is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of $e$ . We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of $ε$ -big excursions and of their endpoints, for all $ε$ in a set whose closure contains $0$ . Finally,...

On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity

Agnieszka Kałamajska (2001)

Colloquium Mathematicae

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We study the functional $I_{f} (u) = \int_{Ω} f (u (x)) d x$ , where u=(u₁, ..., uₘ) and each $u_{j}$ is constant along some subspace $W_{j}$ of ℝⁿ. We show that if intersections of the $W_{j}$ ’s satisfy a certain condition then $I_{f}$ is weakly lower semicontinuous if and only if f is Λ-convex (see Definition 1.1 and Theorem 1.1). We also give a necessary and sufficient condition on ${W_{j}}_{j = 1, . . ., m}$ to have the equivalence: $I_{f}$ is weakly continuous if and only if f is Λ-affine.