Extension of a class of decomposable measures via generalized pseudo-metrics

Abstract This study considers the application of generalized pseudo-metrics to the extension of decomposable measures. We prove that the extension of a non-strict Archimedean t-conorm-based σ-decomposable measure can be formulated as the closure of a subset of a certain generalized pseudo-metric space. We show that the extension via generalized pseudo-metrics is equivalent to the completion of t-conorm-based σ-decomposable measures and the well-known Caratheodory extension.

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