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Sequences of 0's and 1's

Grahame Bennett, Johann Boos, Toivo Leiger (2002)

Studia Mathematica

We investigate the extent to which sequence spaces are determined by the sequences of 0's and 1's that they contain.

Sequences of 0's and 1's: sequence spaces with the separable Hahn property

Maria Zeltser (2007)

Studia Mathematica

In [3] it was discovered that one of the main results in [1] (Theorem 5.2), applied to three spaces, contains a nontrivial gap in the argument, but neither the gap was closed nor a counterexample was provided. In [4] the authors verified that all three above mentioned applications of the theorem are true and stated a problem concerning the topological structure of one of these three spaces. In this paper we answer the problem and give a counterexample to the theorem in doubt. Also we establish a...

Statistical convergence of a sequence of random variables and limit theorems

Sanjoy Ghosal (2013)

Applications of Mathematics

In this paper the ideas of three types of statistical convergence of a sequence of random variables, namely, statistical convergence in probability, statistical convergence in mean of order r and statistical convergence in distribution are introduced and the interrelation among them is investigated. Also their certain basic properties are studied.

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