Convergent sequences of 𝜏-smooth measures

Khurana, Surjit Singh

doi:10.1090/S0002-9939-1977-0435342-4

Convergent sequences of $\tau$-smooth measures
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by Surjit Singh Khurana PDF

Proc. Amer. Math. Soc. 63 (1977), 137-142 Request permission

Abstract:

It is proved that every $\tau$-smooth, group-valued Borel measure on a regular Hausdorff space is regular; also it is proved that if a sequence of $\tau$-smooth Borel measures on a regular Hausdorff space is convergent for regular open sets, then it is convergent for all Borel sets. For a completely regular Hausdorff space, it is proved that if a sequence of Borel $\tau$-smooth measures is convergent for exactly open sets then it is convergent for all Borel sets.

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