Attouch-Wets convergence and Kuratowski convergence on compact sets

Paolo Piccione; Rosella Sampalmieri

Displaying similar documents to “Attouch-Wets convergence and Kuratowski convergence on compact sets”

Function space topologies deriving from hypertopologies and networks

A. Di Concilio, A. Miranda (2001)

Bollettino dell'Unione Matematica Italiana

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In un progetto di generalizzazione delle classiche topologie di tipo «set-open» di Arens-Dugundji introduciamo un metodo generale per produrre topologie in spazi di funzioni mediante l'uso di ipertopologie. Siano $X$ , $Y$ spazi topologici e $C (X, Y)$ l'insieme delle funzioni continue da $X$ verso $Y$ . Fissato un «network» $α$ nel dominio $X$ ed una topologia $τ$ nell'iperspazio $C L (Y)$ del codominio $Y$ si genera una topologia $τ_{α}$ in $C (X, Y)$ richiedendo che una rete $\{f_{λ}\}$ di $C (X, Y)$ converge in $τ_{α}$ ad $f \in C (X, Y)$ se e solo se la rete $\{\bar{f_{λ} (A)}\}$ converge...

A generalization of boundedly compact metric spaces

Gerald Beer, Anna Di Concilio (1991)

Commentationes Mathematicae Universitatis Carolinae

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A metric space $〈 X, d 〉$ is called a $UC$ space provided each continuous function on $X$ into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that $UC$ spaces play relative to the compact metric spaces.

A correction to “Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables”

Yongfeng Wu, Andrew Rosalsky, Andrei Volodin (2017)

Applications of Mathematics

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The authors provide a correction to “Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables”.

Generalizations to monotonicity for uniform convergence of double sine integrals over ℝ̅²₊

Péter Kórus, Ferenc Móricz (2010)

Studia Mathematica

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We investigate the convergence behavior of the family of double sine integrals of the form $\int_{0}^{\infty} \int_{0}^{\infty} f (x, y) s i n u x s i n v y d x d y$ , where (u,v) ∈ ℝ²₊:= ℝ₊ × ℝ₊, ℝ₊:= (0,∞), and f: ℝ²₊ → ℂ is a locally absolutely continuous function satisfying certain generalized monotonicity conditions. We give sufficient conditions for the uniform convergence of the remainder integrals $\int_{a ₁}^{b ₁} \int_{a ₂}^{b ₂}$ to zero in (u,v) ∈ ℝ²₊ as maxa₁,a₂ → ∞ and $b_{j} > a_{j} \geq 0$ , j = 1,2 (called uniform convergence in the regular sense). This implies the uniform convergence of the partial...

Displaying similar documents to “Attouch-Wets convergence and Kuratowski convergence on compact sets”

Function space topologies deriving from hypertopologies and networks

A generalization of boundedly compact metric spaces

A correction to “Some mean convergence and complete convergence theorems for sequences of m -linearly negative quadrant dependent random variables”

Generalizations to monotonicity for uniform convergence of double sine integrals over ℝ̅²₊

A correction to “Some mean convergence and complete convergence theorems for sequences of $m$ -linearly negative quadrant dependent random variables”