mathematics, specifically measure theory, a complex measure generalizes the concept of measure by letting it have complex values. In other words, one...

of notation, total variation measure. If the measure μ {\displaystyle \mu } is complex-valued i.e. is a complex measure, its upper and lower variation...

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

theorem is a result in measure theory that expresses the relationship between two measures defined on the same measurable space. A measure is a set function...

This definition applies mutatis mutandis for a signed or complex measure. The pushforward measure is also denoted as μ ∘ f − 1 {\displaystyle \mu \circ f^{-1}}...

to signed and complex measures. Suppose that μ : Σ → [ − ∞ , + ∞ ] {\displaystyle \mu :\Sigma \to [-\infty ,+\infty ]} is a signed measure. Use the Hahn...

{\displaystyle \sigma } -algebra on X {\displaystyle X} ). A measure/signed measure/complex measure μ {\displaystyle \mu } defined on Σ {\displaystyle \Sigma...

space – Type of topological space Complex measure – Measure with complex values Signed measure – Generalized notion of measure in mathematics Vector-valued...

rather than real numbers. As in the case of ordinary measures, it is possible to integrate complex-valued functions with respect to a PVM; the result of...

In mathematics, two positive (or signed or complex) measures μ {\displaystyle \mu } and ν {\displaystyle \nu } defined on a measurable space ( Ω , Σ )...

pre–metric system French measures), which equals around 1.67 metres, or just under 5 feet 6 inches in imperial measure. The Napoleon complex is named after French...

In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity...

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

such equivalence classes. If μ {\displaystyle \mu } is a signed or complex measure, it is said that μ {\displaystyle \mu } is absolutely continuous with...

a measure space, μ {\displaystyle \mu } a σ-finite positive measure on Σ {\displaystyle \Sigma } and λ {\displaystyle \lambda } a complex measure on...

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...

Riesz–Markov–Kakutani representation theorem. Angular displacement Complex measure Spectral measure Vector measure Riesz–Markov–Kakutani representation theorem Signed...

equilibrium measure μ f {\displaystyle \mu _{f}} . On the other hand, the measure μ f {\displaystyle \mu _{f}} vanishes on closed complex subspaces not...

string η {\displaystyle \eta } is defined to be a local positive or complex measure on ( 0 , + ∞ ) {\displaystyle (0,+\infty )} such that | η | ( 0 , x...

) Let M {\displaystyle M} be a collection of (possibly signed or complex) measures defined on Σ {\displaystyle \Sigma } . The collection M {\displaystyle...

In mathematics, the Mahler measure M ( p ) {\displaystyle M(p)} of a polynomial p ( z ) {\displaystyle p(z)} with complex coefficients is defined as M...

policymakers clearer picture of the outcome of government programs. Measuring poverty is a complex and comprehensive task requiring various methods and approaches...

mathematics in complex analysis, the concept of holomorphic separability is a measure of the richness of the set of holomorphic functions on a complex manifold...

{z}}=x^{2}+y^{2}=1.} The complex unit circle can be parametrized by angle measure θ {\displaystyle \theta } from the positive real axis using the complex exponential...

complete measure (or, more precisely, a complete measure space) is a measure space in which every subset of every null set is measurable (having measure zero)...

is instead some vector space, as with vector measures, complex measures, and projection-valued measures. The domain of a set function may have any number...

education, income and living conditions in a given country to provide a measure of human development which is comparable between countries and over time...

In mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all...

confuse more than they illuminate." Negative probability Signed measure Complex measure Youssef, Saul (2001). "Physics with exotic probability theory"...

between 1994 and 2007 and was inaugurated in December 2007. The building complex measures approximately 290 by 420 m (950 by 1,380 ft), covering an area of more...