A note on almost sure convergence and convergence in measure

P. Kříž; Josef Štěpán

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 1, page 29-40
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Kříž, P., and Štěpán, Josef. "A note on almost sure convergence and convergence in measure." Commentationes Mathematicae Universitatis Carolinae 55.1 (2014): 29-40. <http://eudml.org/doc/260791>.

@article{Kříž2014,
abstract = {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.},
author = {Kříž, P., Štěpán, Josef},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {convergence in measure; almost sure convergence; pointwise compactness; Lusin property; strongly consistent estimators; convergence in measure; almost sure convergence; pointwise compactness; Lusin property; strongly consistent estimators},
language = {eng},
number = {1},
pages = {29-40},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on almost sure convergence and convergence in measure},
url = {http://eudml.org/doc/260791},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Kříž, P.
AU - Štěpán, Josef
TI - A note on almost sure convergence and convergence in measure
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 1
SP - 29
EP - 40
AB - 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.
LA - eng
KW - convergence in measure; almost sure convergence; pointwise compactness; Lusin property; strongly consistent estimators; convergence in measure; almost sure convergence; pointwise compactness; Lusin property; strongly consistent estimators
UR - http://eudml.org/doc/260791
ER -

References

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  1. Asanov M.O., Veličko N.V., Kompaktnye množestva v C p ( X ) , Comment. Math. Univ. Carolinae 22 (1981), 255–266. 
  2. Blackwell D., 10.1214/aop/1176994581, Ann. Probability 8 (1980), 1189–1190. Zbl0451.28001MR0602393DOI10.1214/aop/1176994581
  3. Dunford N., Schwartz J.T., Linear Operators Part I: General Theory, John Wiley & Sons, Inc., New Jersey, 1988. Zbl0635.47001MR1009162
  4. Fremlin D.H., Measure Theory, Vol 4, Topological Measure Spaces, Colchester: Torres Fremlin, 2003. Zbl1166.28001MR2462372
  5. Ionescu Tulcea A., 10.1007/BF00532722, Z. Wahrscheinlichkeitstheorie und verw. Gebiete 26 (1973), 197–205. MR0405102DOI10.1007/BF00532722
  6. Ionescu Tulcea A., 10.1016/S0001-8708(74)80002-2, Advances in Math. 12 (1974), 171–177. Zbl0301.46032MR0405103DOI10.1016/S0001-8708(74)80002-2
  7. Kelley J.L., General Topology, Springer, New York, 1975. Zbl0518.54001MR0370454
  8. Kříž P., How to construct Borel measurable PLIFs?, WDS'11 Proc. of Contr. Papers, Part I, (2011), 43–48. 
  9. Štěpán J., 10.1214/aop/1176996899, Ann. Probability 1 (1973), 712–715. Zbl0263.60013MR0356196DOI10.1214/aop/1176996899

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