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  "body": "\n## Summary\n\nA [[moment problem|CS7TWHY7JM]] is determinate when exactly one measure has the given moments.\nThen the moments determine the measure, and in probability the moments determine the law of a random variable.\nThis justifies the method of moments in limit theorems.\nIf the moments of a sequence of laws converge to those of a determinate law, the laws converge to it.\nDeterminacy holds on bounded sets, and on unbounded sets under growth conditions such as [[Carleman's condition|RVZ831CNYW]].\n\n## Explanations\n\n### L1 human\n\nKnowing all moments of a distribution does not always tell you the distribution.\nWhen it does, the moment problem is called determinate.\nEvery distribution on a bounded interval is determined by its moments.\nSo is the normal distribution, because its moments do not grow too fast.\n",
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