Hardy's criterion: If is a probability distribution supported on , such that , then all its moments are finite, and is the unique distribution with these moments.[1][2][3]
↑ Hardy, G. H. (1917). "On Stieltjes' "problème des moments"". Messenger of Mathematics. 46: 175–182.. Reprinted in Hardy, G. H. (1979). Collected Papers of G. H. Hardy. Vol.VII. Oxford: Oxford University Press. pp.75–83.
↑ Hardy, G. H. (1918). "On Stieltjes' "problème des moments" (continued)". Messenger of Mathematics. 47: 81–88.. Reprinted in Hardy, G. H. (1979). Collected Papers of G. H. Hardy. Vol.VII. Oxford: Oxford University Press. pp.84–91.
Reed, Michael; Simon, Barry (1975), Fourier Analysis, Self-Adjointness, Methods of modern mathematical physics, vol.2, Academic Press, p.341 (exercise 25), ISBN0-12-585002-6
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