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Lebesgue measurable
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Lebesgue measure — In mathematics, the Lebesgue measure, named after Henri Lebesgue, is the standard way of assigning a length, area or volume to subsets of Euclidean space. It is used throughout real analysis, in particular to define Lebesgue integration. Sets… … Wikipedia
Lebesgue integration — In mathematics, the integral of a non negative function can be regarded in the simplest case as the area between the graph of that function and the x axis. Lebesgue integration is a mathematical construction that extends the integral to a larger… … Wikipedia
Measurable function — In mathematics, particularly in measure theory, measurable functions are structure preserving functions between measurable spaces; as such, they form a natural context for the theory of integration. Specifically, a function between measurable… … Wikipedia
Lebesgue's density theorem — In mathematics, Lebesgue s density theorem states that for any Lebesgue measurable set A, the density of A is 1 at almost every point in A. Intuitively, this means that the edge of A, the set of points in A whose neighborhood is partially in A… … Wikipedia
Measurable Riemann mapping theorem — In the mathematical theory of quasiconformal mappings in two dimensions, the measurable Riemann mapping theorem, proved by Morrey (1936, 1938), generalizes the Riemann mapping theorem from conformal to quasiconformal homeomorphisms, and is… … Wikipedia
Lebesgue differentiation theorem — In mathematics, the Lebesgue differentiation theorem is a theorem of real analysis.tatementFor a Lebesgue integrable real valued function f, the indefinite integral is a set function which maps a measurable set A to the Lebesgue integral of f… … Wikipedia
Lebesgue-Stieltjes integration — In measure theoretic analysis and related branches of mathematics, Lebesgue Stieltjes integration generalizes Riemann Stieltjes and Lebesgue integration, preserving the many advantages of the latter in a more general measure theoretic framework.… … Wikipedia
Measurable cardinal — In mathematics, a measurable cardinal is a certain kind of large cardinal number. Contents 1 Measurable 2 Real valued measurable 3 See also 4 References … Wikipedia
Lebesgue's decomposition theorem — In mathematics, more precisely in measure theory, Lebesgue s decomposition theorem is a theorem which states that given mu and u two sigma; finite signed measures on a measurable space (Omega,Sigma), there exist two sigma; finite signed measures… … Wikipedia
Universally measurable set — In mathematics, a subset A of a Polish space X is universally measurable if it is measurable with respect to every complete probability measure on X that measures all Borel subsets of X. In particular, a universally measurable set of reals is… … Wikipedia
