# Moment Problem

In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequences of moments

More generally, one may consider

for an arbitrary sequence of functions Mn.

### Other articles related to "moment problem, moment problems, moments, problems":

Stieltjes Moment Problem
... In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence { mn, n = 0, 1, 2.. ... The essential difference between this and other well-known moment problems is that this is on a half-line, and in the Hamburger moment problem one considers the ...
Moment Problem - Variations
... An important variation is the truncated moment problem, which studies the properties of measures with fixed first k moments (for a finite k) ... Results on the truncated moment problem have numerous applications to extremal problems, optimisation and limit theorems in probability theory ...
Carleman's Condition - Hamburger Moment Problem
... For the Hamburger moment problem (the moment problem on the whole real line), the theorem states the following Let μ be a measure on R such that all the moments are finite ... If then the moment problem for mn is determinate that is, μ is the only measure on R with (mn) as its sequence of moments ...

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