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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
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Average size of the Fourier--Stieltjes transform of the fractal measures
For $0<\theta<1/2$ define $\mu_\theta$ to be the uniform (self-similar) measure on the Cantor set obtained from the dissection pattern $(1-2\theta,\theta)$. For example, when $\theta=1/3$ the $\mu_\th …