P. Kříž, J. Štěpán
A note on almost sure convergence and convergence in measure

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.

Keywords: convergence in measure; almost sure convergence; pointwise compactness; Lusin property; strongly consistent estimators
AMS Subject Classification: 28A20 62F12