We prove that every profinite [Formula: see text]-ary group [Formula: see text] has a unique Haar measure [Formula: see text] and further for every measurable subset [Formula: see text], we have [Formula: see text] where [Formula: see text] and [Formula: see text] are the normalized Haar measures of the profinite groups [Formula: see text] and the Post cover [Formula: see text], respectively.
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Shahryari et al. (2024) studied this question.
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