In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence (m0, m1, m2, ...) be the sequence of moments m n = ∫ 0 1 x n d μ ( x ) {\displaystyle m_{n}=\int _{0}^{1}x^{n}\,d\mu (x)} 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 mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence (m0, m1, m2, ...) be the sequence of moments m n = ∫ 0 1 x n d μ ( x ) {\displaystyle m_{n}=\int _{0}^{1}x^{n}\,d\mu (x)} 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.
Source: Wikipedia "Hausdorff moment problem" · CC BY-SA 4.0
Share this article: X · Bluesky