On the total variation and Hellinger distance between signed measures; an application to product measures

Steerneman, Ton

doi:10.1090/S0002-9939-1983-0702299-0

On the total variation and Hellinger distance between signed measures; an application to product measures
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by Ton Steerneman

Proc. Amer. Math. Soc. 88 (1983), 684-688

DOI: https://doi.org/10.1090/S0002-9939-1983-0702299-0

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Abstract:

Firstly, the Hellinger metric on the set of probability measures on a measurable space is extended to the set of signed measures. An inequality between total variation and Hellinger metric due to Kraft is generalized to the case of signed measures. The inequality is used in order to derive a lower estimate concerning the total variation distance between products of signed measures. The lower bound depends on the total variation norms of the signed measures and the total variation distances between the total variation measures of the single components.

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