{'fraction_non_alphanumeric': 0.019464720194647202, 'fraction_numerical': 0.0, 'mean_word_length': 4.282051282051282, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Metric entropy of convex hulls in Hilbert spaces

Let T ⊆ H be a precompact set and let aco(T ) be its symmetric convex hull. We estimate the size of aco(T ) with respect to metric entropy or the diameter of finite codimensional slices by quantities of T originated in the theory of majorizing measures. Our estimates are best possible for some sets consisting of a sequence of vectors. Supported in part by NSF