What does countable additivity mean?
Definitions for countable additivity
count·able ad·di·tiv·i·ty
This dictionary definitions page includes all the possible meanings, example usage and translations of the word countable additivity.
Wiktionary
countable additivitynoun
The following property of a measure: that the measure of a countable union of disjoint sets is equal to the sum of their measures.
Wikipedia
countable additivity
In mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, μ ( A ∪ B ) = μ ( A ) + μ ( B ) . {\textstyle \mu (A\cup B)=\mu (A)+\mu (B).} If this additivity property holds for any two sets, then it also holds for any finite number of sets, namely, the function value on the union of k disjoint sets (where k is a finite number) equals the sum of its values on the sets. Therefore, an additive set function is also called a finitely-additive set function (the terms are equivalent). However, a finitely-additive set function might not have the additivity property for a union of an infinite number of sets. A σ-additive set function is a function that has the additivity property even for countably infinite many sets, that is, μ ( ⋃ n = 1 ∞ A n ) = ∑ n = 1 ∞ μ ( A n ) . {\textstyle \mu \left(\bigcup _{n=1}^{\infty }A_{n}\right)=\sum _{n=1}^{\infty }\mu (A_{n}).} Additivity and sigma-additivity are particularly important properties of measures. They are abstractions of how intuitive properties of size (length, area, volume) of a set sum when considering multiple objects. Additivity is a weaker condition than σ-additivity; that is, σ-additivity implies additivity. The term modular set function is equivalent to additive set function; see modularity below.
Numerology
Chaldean Numerology
The numerical value of countable additivity in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of countable additivity in Pythagorean Numerology is: 9
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"countable additivity." Definitions.net. STANDS4 LLC, 2024. Web. 27 Jul 2024. <https://www.definitions.net/definition/countable+additivity>.
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