Strong tightness as a condition  of weak and almost sure convergence

Grzegorz Krupa; Wiesław Zieba

Displaying similar documents to “Strong tightness as a condition of weak and almost sure convergence”

On solutions of the difference equation $x_{n + 1} = x_{n - 3} / (- 1 + x_{n} x_{n - 1} x_{n - 2} x_{n - 3})$

Cengiz Cinar, Ramazan Karatas, Ibrahim Yalçınkaya (2007)

Mathematica Bohemica

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We study the solutions and attractivity of the difference equation $x_{n + 1} = x_{n - 3} / (- 1 + x_{n} x_{n - 1} x_{n - 2} x_{n - 3})$ for $n = 0, 1, 2, \dots$ where $x_{- 3}, x_{- 2}, x_{- 1}$ and $x_{0}$ are real numbers such that $x_{0} x_{- 1} x_{- 2} x_{- 3} \neq 1 .$

On a characterization of orthogonality with respect to particular sequences of random variables in $L^{2}$

Umberto Triacca, Andrei Volodin (2010)

Applications of Mathematics

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This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results on equidistant systems of points in a Hilbert space to the case of the space $L^{2} (Ω, ℱ, ℙ)$ of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular sequence of random variables (elements of which are taken from sets of equidistant elements of $L^{2} (Ω, ℱ, ℙ)$ ) to be orthogonal to some other sequence in $L^{2} (Ω, ℱ, ℙ)$ . The result obtained...

A note on k-c-semistratifiable spaces and strong $β$ -spaces

Li-Xia Wang, Liang-Xue Peng (2011)

Mathematica Bohemica

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Recall that a space $X$ is a c-semistratifiable (CSS) space, if the compact sets of $X$ are $G_{δ}$ -sets in a uniform way. In this note, we introduce another class of spaces, denoting it by k-c-semistratifiable (k-CSS), which generalizes the concept of c-semistratifiable. We discuss some properties of k-c-semistratifiable spaces. We prove that a $T_{2}$ -space $X$ is a k-c-semistratifiable space if and only if $X$ has a $g$ function which satisfies the following conditions: (1) For each $x \in X$ , ${x} = ⋂ {g (x, n) : n \in ℕ}$ and $g (x, n + 1) \subseteq g (x, n)$ for each...

On the convergence of certain sums of independent random elements

Juan Carlos Ferrando (2002)

Commentationes Mathematicae Universitatis Carolinae

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In this note we investigate the relationship between the convergence of the sequence ${S_{n}}$ of sums of independent random elements of the form $S_{n} = \sum_{i = 1}^{n} ε_{i} x_{i}$ (where $ε_{i}$ takes the values $\pm 1$ with the same probability and $x_{i}$ belongs to a real Banach space $X$ for each $i \in ℕ$ ) and the existence of certain weakly unconditionally Cauchy subseries of $\sum_{n = 1}^{\infty} x_{n}$ .

Displaying similar documents to “Strong tightness as a condition of weak and almost sure convergence”

On solutions of the difference equation x n + 1 = x n - 3 / ( - 1 + x n x n - 1 x n - 2 x n - 3 )

On a characterization of orthogonality with respect to particular sequences of random variables in L 2

A note on k-c-semistratifiable spaces and strong β -spaces

On the convergence of certain sums of independent random elements

On solutions of the difference equation $x_{n + 1} = x_{n - 3} / (- 1 + x_{n} x_{n - 1} x_{n - 2} x_{n - 3})$

On a characterization of orthogonality with respect to particular sequences of random variables in $L^{2}$

A note on k-c-semistratifiable spaces and strong $β$ -spaces