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In mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of any measurable set is measurable.
The use of the word measure, in the sense of a measuring instrument, only survives in the phrase tape measure, an instrument that can be used to measure but cannot be used to draw straight lines. As can be seen in the photographs on this page, a two-metre carpenter's rule can be folded down to a length of only 20 centimetres, to easily fit in a ...
The relationship between measurability and weak measurability is given by the following result, known as Pettis' theorem or Pettis measurability theorem. Function f is almost surely separably valued (or essentially separably valued ) if there exists a subset N ⊆ X with μ ( N ) = 0 such that f ( X \ N ) ⊆ B is separable.
Measurability (collectability) relates to the ease of acquisition or measurement of the trait. In addition, acquired data should be in a form that permits subsequent processing and extraction of the relevant feature sets. Performance relates to the accuracy, speed, and robustness of technology used (see performance section for more details).
Countable additivity of a measure : The measure of a countable disjoint union is the same as the sum of all measures of each subset.. Let be a set and a σ-algebra over . A set function from to the extended real number line is called a measure if the following conditions hold:
A thesaurus (pl.: thesauri or thesauruses), sometimes called a synonym dictionary or dictionary of synonyms, is a reference work which arranges words by their meanings (or in simpler terms, a book where one can find different words with similar meanings to other words), [1] [2] sometimes as a hierarchy of broader and narrower terms, sometimes simply as lists of synonyms and antonyms.
This category is not for articles about concepts and things but only for articles about the words themselves.Please keep this category purged of everything that is not actually an article about a word or phrase.
any measurable space, so it is a synonym for a measurable space as defined above [1] a measurable space that is Borel isomorphic to a measurable subset of the real numbers (again with the Borel σ {\displaystyle \sigma } -algebra) [ 3 ]