On the partition property of measures on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$P_\mathcal{H} \lambda $ " id="E1"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi>ℋ</mml:mi></mml:msub><mml:mi>λ</mml:mi></mml:mrow></mml:math>
International journal of mathematics and mathematical sciences