absolutely continuous measure

абсолютно непрерывная мера

English-Russian scientific dictionary. 2008.

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  • Continuous probability distribution — In probability theory, a probability distribution is called continuous if its cumulative distribution function is continuous. That is equivalent to saying that for random variables X with the distribution in question, Pr [ X = a ] = 0 for all… …   Wikipedia

  • Singular measure — In mathematics, two positive (or signed or complex) measures μ and ν defined on a measurable space (Ω, Σ) are called singular if there exist two disjoint sets A and B in Σ whose union is Ω such that μ is zero on all measurable subsets of B while… …   Wikipedia

  • Information theory and measure theory — Measures in information theory = Many of the formulas in information theory have separate versions for continuous and discrete cases, i.e. integrals for the continuous case and sums for the discrete case. These versions can often be generalized… …   Wikipedia

  • Strictly positive measure — In mathematics, strict positivity is a concept in measure theory. Intuitively, a strictly positive measure one that is nowhere zero , or that it is zero only on points .DefinitionLet ( X , T ) be a Hausdorff topological space and let Sigma; be a… …   Wikipedia

  • Quasi-invariant measure — In mathematics, a quasi invariant measure mu; with respect to a transformation T , from a measure space X to itself, is a measure which, roughly speaking, is multiplied by a numerical function by T . An important class of examples occurs when X… …   Wikipedia

  • List of integration and measure theory topics — This is a list of integration and measure theory topics, by Wikipedia page.Intuitive foundations*Length *Area *Volume *Probability *Moving averageRiemann integral*Riemann sum *Riemann Stieltjes integral *Bounded variation *Jordan contentImproper… …   Wikipedia

  • Forward measure — A T forward measure is a pricing measure absolutely continuous with respect to a risk neutral measure but rather than using the money market as numeraire, it uses a bond with maturity T. Mathematical Definition Let D(T) = expleft( int 0^T r(u) du …   Wikipedia

  • Equivalence (measure theory) — In mathematics, and specifically in measure theory, equivalence is a notion of two measures being the same . Two measures are equivalent if they have the same null sets.DefinitionLet ( X , Σ) be a measurable space, and let μ , ν : Σ → [0, +∞] be… …   Wikipedia

  • Signed measure — In mathematics, signed measure is a generalization of the concept of measure by allowing it to have negative values. Some authors may call it a charge,[1] by analogy with electric charge, which is a familiar distribution that takes on positive… …   Wikipedia

  • Absolute continuity — In mathematics, the relationship between the two central operations of calculus, differentiation and integration, stated by fundamental theorem of calculus in the framework of Riemann integration, is generalized in several directions, using… …   Wikipedia

  • Dirac delta function — Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… …   Wikipedia


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