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

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