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arXiv · 1303.2368

An Arzel\`a-Ascoli theorem for the Hausdorff measure of noncompactness

Ben Berckmoes
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Abstract

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.

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Ben Berckmoes. 2013-03-10. An Arzel\`a-Ascoli theorem for the Hausdorff measure of noncompactness. https://arxiv.org/abs/1303.2368

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