### Topological and measure properties of some self-similar sets

DOI: http://dx.doi.org/10.12775/TMNA.2015.075

#### Abstract

self-similar set $K(\Sigma ;q)=\bigg\\sum\limits_n=0^\infty

a_nq^n:(a_n)_n\in \omega \in \Sigma ^\omega \bigg\$, which is the

unique compact solution of the equation $K=\Sigma +qK$. The obtained results

are applied to studying partial sumsets $E(x)=\bigg\\sum\limits_n=0^\infty

x_n\varepsilon _n:(\varepsilon _n)_n\in \omega \in \0,1\^\omega %

\bigg\$ of multigeometric sequences $x=(x_n)_n\in \omega $. Such sets

were investigated by Ferens, Mor\'an, Jones and others. The aim of the

paper is to unify and deepen existing piecemeal results.

#### Keywords

#### References

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