An Arzel\`a-Ascoli theorem for the Hausdorff measure of noncompactness
classification
🧮 math.FA
keywords
measurea-ascoliarzelhausdorffnoncompactnessspacetheoremchebyshev
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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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