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- Hausdorff_moment_problem abstract "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 momentsof 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.The essential difference between this and other well-known moment problems is that this is on a bounded interval, whereas in the Stieltjes moment problem one considers a half-line [0, ∞), and in the Hamburger moment problem one considers the whole line (−∞, ∞).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 equationfor all n,k ≥ 0. Here, Δ is the difference operator given byThe necessity of this condition is easily seen by the identitywhich is ≥ 0, being the integral of an almost sure non-negative function.For example, it is necessary to have".
- Hausdorff_moment_problem wikiPageExternalLink MomentProblem.html.
- Hausdorff_moment_problem wikiPageID "3216387".
- Hausdorff_moment_problem wikiPageRevisionID "564507133".
- Hausdorff_moment_problem hasPhotoCollection Hausdorff_moment_problem.
- Hausdorff_moment_problem subject Category:Mathematical_problems.
- Hausdorff_moment_problem subject Category:Probability_theory.
- Hausdorff_moment_problem subject Category:Theory_of_probability_distributions.
- Hausdorff_moment_problem type Abstraction100002137.
- Hausdorff_moment_problem type Attribute100024264.
- Hausdorff_moment_problem type Condition113920835.
- Hausdorff_moment_problem type Difficulty114408086.
- Hausdorff_moment_problem type MathematicalProblems.
- Hausdorff_moment_problem type Problem114410605.
- Hausdorff_moment_problem type State100024720.
- Hausdorff_moment_problem comment "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 momentsof some Borel measure μ supported on the closed unit interval [0, 1].".
- Hausdorff_moment_problem label "Hausdorff moment problem".
- Hausdorff_moment_problem sameAs m.08zz04.
- Hausdorff_moment_problem sameAs Q5682821.
- Hausdorff_moment_problem sameAs Q5682821.
- Hausdorff_moment_problem sameAs Hausdorff_moment_problem.
- Hausdorff_moment_problem wasDerivedFrom Hausdorff_moment_problem?oldid=564507133.
- Hausdorff_moment_problem isPrimaryTopicOf Hausdorff_moment_problem.