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Modular functions on multilattices

Anna Avallone (2002)

Czechoslovak Mathematical Journal

We prove that every modular function on a multilattice L with values in a topological Abelian group generates a uniformity on L which makes the multilattice operations uniformly continuous with respect to the exponential uniformity on the power set of L .

Moments of vector measures and Pettis integrable functions

Miloslav Duchoň (2011)

Czechoslovak Mathematical Journal

Conditions, under which the elements of a locally convex vector space are the moments of a regular vector-valued measure and of a Pettis integrable function, both with values in a locally convex vector space, are investigated.

Moving averages

S. V. Butler, J. M. Rosenblatt (2008)

Colloquium Mathematicae

In ergodic theory, certain sequences of averages A k f may not converge almost everywhere for all f ∈ L¹(X), but a sufficiently rapidly growing subsequence A m k f of these averages will be well behaved for all f. The order of growth of this subsequence that is sufficient is often hyperexponential, but not necessarily so. For example, if the averages are A k f ( x ) = 1 / ( 2 k ) j = 4 k + 1 4 k + 2 k f ( T j x ) , then the subsequence A k ² f will not be pointwise good even on L , but the subsequence A 2 k f will be pointwise good on L¹. Understanding when the hyperexponential...

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