Hausdorff moment problem
In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence { mn : n = 0, 1, 2, ... }be the sequence of moments of some Borel measure μ supported on the closed unit interval [0, 1]. In the case m0 = 1, this is equivalent to the existence of a random variable X supported on [0, 1], such that E Xn = mn. In 1921, Hausdorff showed that { mn : n = 0, 1, 2, ... } is such a moment sequence if and only if the sequence is completely monotonic, i.e., its difference sequences satisfy the equation
known for
Wikipage disambiguates
Wikipage redirect
primaryTopic
Hausdorff moment problem
In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence { mn : n = 0, 1, 2, ... }be the sequence of moments of some Borel measure μ supported on the closed unit interval [0, 1]. In the case m0 = 1, this is equivalent to the existence of a random variable X supported on [0, 1], such that E Xn = mn. In 1921, Hausdorff showed that { mn : n = 0, 1, 2, ... } is such a moment sequence if and only if the sequence is completely monotonic, i.e., its difference sequences satisfy the equation
has abstract
In mathematics, the Hausdorff ...... ample, it is necessary to have
@en
Link from a Wikipage to an external page
Wikipage page ID
Wikipage revision ID
725,113,636
comment
In mathematics, the Hausdorff ...... sequences satisfy the equation
@en
label
Hausdorff moment problem
@en