The space of Radon measure measures on the closed unit interval is the free topological vector space over the interval. It has universal property that evey continuous function on the interval has a unique extension to a continuous linear mapping. This has zillions of generalisations---Radon measures on compacta, bounded Radon measures on a completely regular space, uniform measures on a uniform space and, and ...
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The space of Radon measure on the closed unit interval is the free topological vector space over the interval. It has universal property that evey continuous function on the interval has a unique extension to a continuous linear mapping. This has zillions of generalisations---Radon measures on compacta, bounded Radon measures on a completely regular space, uniform measures on a uniform space and, and ... |
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