Definitions for counting measure
count·ing mea·sure

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1. counting measurenoun

   A positive measure which, for each subset of a given measure space, assigns a value equal to the number of points in that subset.

WikipediaRate this definition:0.0 / 0 votes

1. Counting measure

   In mathematics, specifically measure theory, the counting measure is an intuitive way to put a measure on any set – the "size" of a subset is taken to be the number of elements in the subset if the subset has finitely many elements, and infinity ∞ {\displaystyle \infty } if the subset is infinite.The counting measure can be defined on any measurable space (that is, any set X {\displaystyle X} along with a sigma-algebra) but is mostly used on countable sets.In formal notation, we can turn any set X {\displaystyle X} into a measurable space by taking the power set of X {\displaystyle X} as the sigma-algebra Σ ; {\displaystyle \Sigma ;} that is, all subsets of X {\displaystyle X} are measurable sets. Then the counting measure μ {\displaystyle \mu } on this measurable space ( X , Σ ) {\displaystyle (X,\Sigma )} is the positive measure Σ → [ 0 , + ∞ ] {\displaystyle \Sigma \to [0,+\infty ]} defined by for all A ∈ Σ , {\displaystyle A\in \Sigma ,} where | A | {\displaystyle \vert A\vert } denotes the cardinality of the set A . {\displaystyle A.} The counting measure on ( X , Σ ) {\displaystyle (X,\Sigma )} is σ-finite if and only if the space X {\displaystyle X} is countable.

WikidataRate this definition:0.0 / 0 votes

1. Counting measure

   In mathematics, the counting measure is an intuitive way to put a measure on any set: the "size" of a subset is taken to be the number of elements in the subset, if the subset has finitely many elements, and ∞ if the subset is infinite. The counting measure can be defined on any measurable set, but is mostly used on countable sets. In formal notation, we can make any set into a measurable space by taking the sigma-algebra of measurable subsets to consist of all subsets of . Then the counting measure on this measurable space is the positive measure defined by for all, where denotes the cardinality of the set . The counting measure on is σ-finite if and only if the space is countable.

How to pronounce counting measure?

1. Alex

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   British

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   Australian

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How to say counting measure in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of counting measure in Chaldean Numerology is: 6

2. Pythagorean Numerology

   The numerical value of counting measure in Pythagorean Numerology is: 5

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Counting_Measure
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Counting_Measure
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=counting measure