Continuity of spectral averaging

We consider averages $κ$ of spectral measures of rank one perturbations with respect to a $σ$-finite measure $ν$. It is examined how various degrees of continuity of $ν$ with respect to $α$-dimensional Hausdorff measures ($0 \leq α\leq 1$) are inherited by $κ$. This extends Kotani's trick where $ν$ is simply the Lebesgue measure.

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