The size of singular component and shift inequalities.(English)Zbl 0946.60008

The question of how large can be the size of singular component of translates $$\mu^{\infty}_h$$ of product probability $$\mu^{\infty}$$ is investigated in terms of Fisher information. Shift inequalities of the form $S_h(\mu^{\infty}(A))\leq \mu^{\infty}_h(A)\leq R_h(\mu^{\infty}(A))$ are obtained for suitable functions $$R_h$$ and $$S_h.$$

MSC:

 6e+06 Probability distributions: general theory
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References:

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