Displaying similar documents to “Beyond Lebesgue and Baire: generic regular variation”

Very slowly varying functions. II

N. H. Bingham, A. J. Ostaszewski (2009)

Colloquium Mathematicae

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This paper is a sequel to papers by Ash, Erdős and Rubel, on very slowly varying functions, and by Bingham and Ostaszewski, on foundations of regular variation. We show that generalizations of the Ash-Erdős-Rubel approach-imposing growth restrictions on the function h, rather than regularity conditions such as measurability or the Baire property-lead naturally to the main result of regular variation, the Uniform Convergence Theorem.

On G δ -spaces

Zdeněk Frolík (1959)

Czechoslovak Mathematical Journal

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A Borel extension approach to weakly compact operators on C 0 ( T )

Thiruvaiyaru V. Panchapagesan (2002)

Czechoslovak Mathematical Journal

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Let X be a quasicomplete locally convex Hausdorff space. Let T be a locally compact Hausdorff space and let C 0 ( T ) = { f T → I , f is continuous and vanishes at infinity } be endowed with the supremum norm. Starting with the Borel extension theorem for X -valued σ -additive Baire measures on T , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map u C 0 ( T ) → X to be weakly compact.