In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff...

In mathematics, the Radon–Nikodym theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable...

Radon is a chemical element; it has symbol Rn and atomic number 86. It is a radioactive noble gas and is colorless and odorless. Of the three naturally...

dg(x)} for all continuous functions  f . The functional I defines a Radon measure on [a, b]. This functional can then be extended to the class of all...

Johann Karl August Radon ([ˈʁaːdɔn]; 16 December 1887 – 25 May 1956) was an Austrian mathematician. His doctoral dissertation was on the calculus of variations...

necessarily a Radon measure). Lebesgue measure is an example of a positive Radon measure. One particularly important class of Radon measures are those that...

Lebesgue measure Lebesgue integration Lebesgue's density theorem Counting measure Complete measure Haar measure Outer measure Borel regular measure Radon measure...

include: Borel measure, Jordan measure, ergodic measure, Gaussian measure, Baire measure, Radon measure, Young measure, and Loeb measure. In physics an...

probability measure that is neither inner regular nor outer regular. Borel regular measure Radon measure Regularity theorem for Lebesgue measure Ambrosio...

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...

In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional)...

λ(G \ A) = λ(A \ F) = 0. Lebesgue measure is both locally finite and inner regular, and so it is a Radon measure. Lebesgue measure is strictly positive on non-empty...

constant, a locally integrable function or, in more general settings, a Radon measure. In the first case, the constant, known as the rate or intensity, is...

topological group. If μ and ν are Radon measures on G, then their convolution μ∗ν is defined as the pushforward measure of the group action and can be written...

The health effects of radon are harmful, and include an increased chance of lung cancer. Radon is a radioactive, colorless, odorless, tasteless noble gas...

Radon mitigation is any process used to reduce radon gas concentrations in the breathing zones of occupied buildings, or radon from water supplies. Radon...

natural topology, and a (Radon) measure is defined as a continuous linear functional on this space. The value of a measure at a compactly supported function...

the total variation metric coincides with the Radon metric. If μ and ν are both probability measures, then the total variation distance is also given...

compact closure, so is not an outer measure.) Cartan introduced another way of constructing Haar measure as a Radon measure (a positive linear functional on...

both inner regular, outer regular, and locally finite, it is called a Radon measure. The real line R {\displaystyle \mathbb {R} } with its usual topology...

support, and the measures can be Baire measures or regular Borel measures or Radon measures or signed measures or complex measures. The statement of...

general version in measure theory is the following: Theorem — Let X be a locally compact Hausdorff space equipped with a finite Radon measure μ, and let Y be...

France Johann Radon, Austrian mathematician Radon transform, a type of mathematical transform Radon measure, a type of mathematical measure Radon space, a...

condition to be an inner regular measure, since singleton sets such as {x} are always compact. Hence, δx is also a Radon measure. Assuming that the topology...

^{n}(K)\mid K\subseteq A,K{\text{ is compact}}\},} so Gaussian measure is a Radon measure; is not translation-invariant, but does satisfy the relation d...

continuity of measures. These two notions are generalized in different directions. The usual derivative of a function is related to the Radon–Nikodym derivative...

necessarily a Radon measure). Lebesgue measure is an example of a positive Radon measure. One particularly important class of Radon measures are those that...

some Radon measure. Generally, when the term Dirac delta function is used, it is in the sense of distributions rather than measures, the Dirac measure being...

variation if its distributional derivative is a vector-valued finite Radon measure. One of the most important aspects of functions of bounded variation...

In measure theory, a radonifying function (ultimately named after Johann Radon) between measurable spaces is one that takes a cylinder set measure (CSM)...