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

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 Carathéodory extension.