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For example, sin(x) dx is a real-valued Radon measure, but is not even an extended signed measure as it cannot be written as the difference of two measures at least one of which is finite. Some authors use the preceding approach to define positive Radon measures to be the positive linear forms on K (X). [4]
This is a list of integration and measure theory topics, ... Outer measure; Borel regular measure; Radon measure; ... Examples of contour integration;
A measure is a set function that assigns a consistent magnitude to the measurable subsets of a measurable space. Examples of a measure include area and volume, where the subsets are sets of points; or the probability of an event, which is a subset of possible outcomes within a wider probability space.
Other 'named' measures used in various theories include: Borel measure, Jordan measure, ergodic measure, Gaussian measure, Baire measure, Radon measure, Young measure, and Loeb measure. In physics an example of a measure is spatial distribution of mass (see for example, gravity potential), or another non-negative extensive property, conserved ...
A Radon space, named after Johann Radon, is a topological space on which every Borel probability measure on M is inner regular. Since a probability measure is globally finite, and hence a locally finite measure, every probability measure on a Radon space is also a Radon measure. In particular a separable complete metric space (M, d) is a Radon ...
Radon gas in the natural gas streams concentrate as NORM in gas processing activities. Radon decays to lead-210, then to bismuth-210, polonium-210 and stabilizes with lead-206. Radon decay elements occur as a shiny film on the inner surface of inlet lines, treating units, pumps and valves associated with propylene, ethane and propane processing ...
The Lebesgue–Stieltjes measure is a regular Borel measure, and conversely every regular Borel measure on the real line is of this kind. Lebesgue–Stieltjes integrals , named for Henri Leon Lebesgue and Thomas Joannes Stieltjes , are also known as Lebesgue–Radon integrals or just Radon integrals , after Johann Radon , to whom much of the ...
Lebesgue measure on Euclidean space is locally finite. By definition, any Radon measure is locally finite. The counting measure is sometimes locally finite and sometimes not: the counting measure on the integers with their usual discrete topology is locally finite, but the counting measure on the real line with its usual Borel topology is not.