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Displaying similar documents to “On the convergence of certain sums of independent random elements”

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...

On the classes of hereditarily ℓ p Banach spaces

Parviz Azimi, A. A. Ledari (2006)

Czechoslovak Mathematical Journal

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Let X denote a specific space of the class of X α , p Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily ℓ p Banach spaces. We show that for p > 1 the Banach space X contains asymptotically isometric copies of ℓ p . It is known that any member of the class is a dual space. We show that the predual of X contains isometric copies of ℓ q where 1 p + 1 q = 1 . For p = 1 it is known that the predual of the Banach space X contains asymptotically isometric copies of...