We consider a sequence <mml:math alttext="$\left\{ {\mu _n } \right\}$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msub><mml:mi>&#x3BC;</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math> of (nonnegative) measures on a general measurable space <mml:math alttext="$\left( {X,\mathcal{B}} \right)$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>&#x212C;</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>. We establish sufficient conditions for setwise convergence and convergence in total variation.

International Journal of Stochastic Analysis

On the setwise convergence of sequences of measures

Abstract

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