MEASURABLEFUNCTION

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 spaces is said to be measurable if the preimage of each measurable set is measurable, analogous to the situation of continuous functions between topological spaces.

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measurable function

Noun

  1. Any well-behaved function of real numbers between measurable spaces.
  2. If a function's codomain is a topological space and the function's domain is a measurable space, then the function is measurable if the inverse image of every open set in its codomain is a measurable set in its domain.


The above text is a snippet from Wiktionary: measurable function
and as such is available under the Creative Commons Attribution/Share-Alike License.

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