Construction of regular non-atomic strictly-positive measures in second-countable non-atomic locally compact Hausdorff spaces
This paper presents a constructive proof of the existence of a regular non-atomic strictly-positive measure on any second-countable non-atomic locally compact Hausdorff space. This construction involves a sequence of finitely-additive set functions defined recursively on an ascending sequence of rings of subsets with a set function limit that is extendable to a measure with the desired properties. Non-atomicity of the space provides a meticulous way to ensure that the set function limit is σ-additive.
regular measure; non-atomic measure; strictly-positive measure; locally compact spaces; non-atomic spaces; Polish spaces; regular spaces; second-countable spaces
2. P. Mikusiński, On the completion of measures, Arch. Math. (Basel) 50 (1988), 259–263.
3. M.E. Munroe, Introduction to Measure and Integration, Addison-Wesley, Cambridge, Mass., 1953.
4. W. Rudin, Real and Complex Analysis, 3rd Edition, McGraw-Hill, New York, 1987.
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