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arXiv:1303.2368 [math.FA]AbstractReferencesReviewsResources

An Arzelà-Ascoli theorem for the Hausdorff measure of noncompactness

Ben Berckmoes

Published 2013-03-10, updated 2013-03-14Version 2

We generalize the Arzel\`a-Ascoli theorem in the space of continuous maps on a compact interval with values in Euclidean N-space by providing a quantitative link between the Hausdorff measure of noncompactness in this space and a natural measure of non-uniform equicontinuity. The proof hinges upon a classical result of Jung's on the Chebyshev radius.

Comments: 6 pages
Categories: math.FA
Subjects: 46B50
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