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.
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
Keywords: convergence in measure; almost sure convergence; pointwise compactness; Lusin property; strongly consistent estimators
@article{CMUC_2014_55_1_a3,
author = {K\v{r}{\'\i}\v{z}, P. and \v{S}t\v{e}p\'an, J.},
title = {A note on almost sure convergence and convergence in measure},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {29--40},
year = {2014},
volume = {55},
number = {1},
mrnumber = {3160824},
zbl = {06383783},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2014_55_1_a3/}
}
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/