Geodesic
A note on almost sure convergence and convergence in measure
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 1, pp. 29-40.

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The present article studies the conditions under which the almost everywhere convergence and the convergence in measure coincide. An application in the statistical estimation theory is outlined as well.
Classification : 28A20, 60B05, 60F05, 60F15, 62C10, 62F12
Keywords: convergence in measure; almost sure convergence; pointwise compactness; Lusin property; strongly consistent estimators 
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     title = {A note on almost sure convergence and convergence in measure},
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Kříž, P.; Štěpán, J. A note on almost sure convergence and convergence in measure. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 1, pp. 29-40. http://geodesic.mathdoc.fr/item/CMUC_2014__55_1_a3/