In mathematics, more specifically measure theory, there are various notions of the convergence of measures. For an intuitive general sense of what is meant by convergence in measure, consider a sequence of measures on a space, sharing a common collection of measurable sets. Such a sequence might represent an attempt to construct 'better and better' approximations to a desired measure that is difficult to obtain directly. The meaning of 'better and better' is subject to all the usual caveats for taking limits; for any error tolerance we require there be sufficiently large for to ensure the 'difference' between and is smaller than . Various notions of convergence specify precisely what the word 'difference' should mean in that description; these notions are not equivalent to one another, and vary in strength.
Three of the most common notions of convergence are described below.
Read more about Convergence Of Measures: Informal Descriptions, Total Variation Convergence of Measures, Strong Convergence of Measures, Weak Convergence of Measures
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