{'fraction_non_alphanumeric': 0.049315068493150684, 'fraction_numerical': 0.0013698630136986301, 'mean_word_length': 3.6265822784810124, 'pattern_counts': {'":': 0, '<': 2, '<?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}}
SOME REMARKS ON MEASURES ON NONCOMPACT SEMISIMPLE LIE GROUPS

This paper answers a question posed by K. R. Parthasarathy: Let X be a symmetric space of non-compact type and G the connected component of the group of isometries of X. Let m be the canonical G-invariant measure on X and E a Borel set in X such that E is compact and 0 < m(E) < ∞. If μ,ν are probability measures on X such that μ(g ⋅ E) = ν(g ⋅ E) for all g ∈ G, then is μ = ν? We answer the question in the affirmative (Theorem A) and also find that the condition “E is compact” is unnecessary. A special case of this problem (under the condition that μ and ν are K-invariant probabilities on X, where K is a maximal compact subgroup of G) was settled by I. K. Rana.