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

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 ∈ X , { x } = ⋂ { g ( x , n ) : n ∈ ℕ } and g ( x , n + 1 ) ⊆ g ( x , n ) for each...