On the dimension of self-similar sets

Károly Simon, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We extend a theorem of Falconer to give a complete result on the dimension and Lebesgue measure of typical self-similar attractors on the line. Further, we present some examples to point out that in higher dimensions, one cannot expect the same result in this generality.

Original languageEnglish
Pages (from-to)59-65
Number of pages7
Issue number1
StatePublished - 2002
Externally publishedYes

Bibliographical note

Funding Information:
Research of Simon was supported in part by the OTKA foundation grant T032022. Research of Solomyak was supported in part by NSF grant #DMS 9800786.


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