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arXiv · 1806.06273

On the Discrepancy Normed Space of Event Sequences for Threshold-based Sampling

Bernhard A. Moser
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Abstract

Recalling recent results on the characterization of threshold-based sampling as quasi-isometric mapping, mathematical implications on the metric and topological structure of the space of event sequences are derived. In this context, the space of event sequences is extended to a normed space equipped with Hermann Weyl's discrepancy measure. Sequences of finite discrepancy norm are characterized by a Jordan decomposition property. Its dual norm turns out to be the norm of total variation. As a by-product a measure for the lack of monotonicity of sequences is obtained. A further result refers to an inequality between the discrepancy norm and total variation which resembles Heisenberg's uncertainty relation.

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Bernhard A. Moser. 2018-06-16. On the Discrepancy Normed Space of Event Sequences for Threshold-based Sampling. https://arxiv.org/abs/1806.06273

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