=+31.6. Suppose that u and F are related by (31.18). If F is not absolutely continuous, then
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=+31.6. Suppose that u and F are related by (31.18). If F is not absolutely continuous, then p( A) > 0 for some set A of Lebesgue measure 0. It is an interesting fact, however, that almost all translates of A must have u-measure 0. From Fubini's theorem and the fact that À is invariant under translation and reflection through 0, show that, if A( A) = 0 and u is o-finite, then p( A +x) =0 for x outside a set of Lebesgue measure 0.
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Probability And Measure Wiley Series In Probability And Mathematical Statistics
ISBN: 9788126517718
3rd Edition
Authors: Patrick Billingsley
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