Radon measure: Mathematics, Measure, Sigma Algebra, Borel Set, Hausdorff Space, Locally Finite Inner Regular Topological Continuous Function

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics (specifically, measure theory), a Radon measure, named after Johann Radon, is a measure on the ¿-algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular.A common problem is to find a good notion of a measure on a topological space that is compatible with the topology in some sense. One way to do this is to define a measure on the Borel sets of the topological space. In general there are several problems with this: for example, such a measure may not have a well defined support. Another approach to measure theory is to restrict to locally compact Hausdorff spaces, and only consider the measures that correspond to positive linear functionals on the space of continuous functions with compact support (some authors use this as the definition of a Radon measure). This produces a good theory with no pathological problems, but does not apply to spaces that are not locally compact.