Geodesic
Application of a Weierstrass Theorem to the Convergence of Moments
Canadian mathematical bulletin, Tome 12 (1969) no. 1, pp. 86-90

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we apply a well-known theorem due to Weierstrass to show that under certain conditions convergence in distribution of a sequence of distribution functions implies the convergence of moments.This note may be understood by an undergraduate student who has an introductory course of complex variables and a second course of statistics. 
Chan, L.K.; Mead, E.R. Application of a Weierstrass Theorem to the Convergence of Moments. Canadian mathematical bulletin, Tome 12 (1969) no. 1, pp. 86-90. doi: 10.4153/CMB-1969-010-2
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