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Certain transformations $$T_\omega$$ and Lebesgue measurable sets of positive measure. (English) Zbl 0953.28002
Let $$\Omega$$ be a metric space, $$\omega _n \rightarrow \omega _0$$ in $$\Omega$$ and $$\alpha _n \rightarrow \alpha _0 \not = 0$$ in $$\mathbb R$$. Let $$T_{\omega _n}$$ be transformations of $$\mathbb R^N$$ into $$\mathbb R^N$$. Conditions are studied in order to guarantee that for every set $$A$$ of positive Lebesgue measure in $$\mathbb R^N$$, the set $\frac 1{\alpha _0} A \cap T_{\alpha_1}\Big (\frac {1}{\alpha _{n_1}}A\Big) \cap T_{\alpha _2} \Big (\frac {1}{\alpha _{n_2}}A\Big)\cap \ldots \cap T_{\alpha _p} \Big (\frac 1{\alpha _{n_p}} A\Big)$ is a set of positive Lebesgue measure for all large enough $$n_i$$.
Reviewer: V.Zizler (Praha)
##### MSC:
 28A05 Classes of sets (Borel fields, $$\sigma$$-rings, etc.), measurable sets, Suslin sets, analytic sets
##### Keywords:
Lebesgue measure transformations
Full Text:
##### References:
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