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Limit measures on second countable locally compact regular spaces Lin, Jung-Fang

Abstract

A. Appert proved in [2] that every sequence of strong measures on a separable weakly locally compact metrizable space has a subsequence converging in the sense of Δ to a strong measure. We extend this result to a second countable locally compact regular space. A. Appert also proved that on a weakly locally compact metrizable space, a sequence of strong measures converges in the sense of Δ to a strong measure if it converges in the sense of Δ₁to that strong measure. In [3], D. J. H. Garling extended this result to a sequence of monotone set functions on a weakly locally compact Hausdorff space under certain conditions. We show that this result still holds on a locally compact regular space with the same conditions.

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