Displaying similar documents to “A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube”

I and I * -convergence in topological spaces

Benoy Kumar Lahiri, Pratulananda Das (2005)

Mathematica Bohemica

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We extend the idea of I -convergence and I * -convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.

Strong tightness as a condition of weak and almost sure convergence

Grzegorz Krupa, Wiesław Zieba (1996)

Commentationes Mathematicae Universitatis Carolinae

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A sequence of random elements { X j , j ∈ J } is called strongly tight if for an arbitrary ϵ > 0 there exists a compact set K such that P ⋂ j ∈ J [ X j ∈ K ] > 1 - ϵ . For the Polish space valued sequences of random elements we show that almost sure convergence of { X n } as well as weak convergence of randomly indexed sequence { X τ } assure strong tightness of { X n , n ∈ ℕ } . For L 1 bounded Banach space valued asymptotic martingales strong tightness also turns out to the sufficient condition of convergence. A sequence of r.e. { X n , n ∈ ℕ } is said to converge essentially...