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  "body": "\n## Summary\n\nA [[moment problem|CS7TWHY7JM]] is indeterminate when at least two different measures have the same moments.\nIt is the failure of [[determinacy|H0GY2J14CA]], and it can only happen when the support is unbounded.\nIn the indeterminate Hamburger case the solutions form an infinite convex set, described by the Nevanlinna parametrization.\n[[Krein's condition|Q401KCEKNZ]] is a test for indeterminacy in terms of a density.\n\n## Explanations\n\n### L1 human\n\nSometimes two genuinely different distributions have exactly the same mean, the same variance, and the same moments of every order.\nThen the moments alone cannot tell them apart, and the moment problem is called indeterminate.\nThis happens for distributions with very heavy tails, such as the log-normal distribution.\nIt never happens for distributions on a bounded interval.\n",
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