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Radon measures have an alternative definition in terms of linear functionals on the locally convex space of continuous functions with compact support. en.wikipedia.org

However, the theory of locally convex spaces is not pre-supposed and the requisite material is developed in a short appendix. en.wikipedia.org

Note that the two notions of boundedness coincide for locally convex spaces. en.wikipedia.org

A locally convex space is then defined to be a vector space along with a family of seminorms on. en.wikipedia.org

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