SELF-AFFINE SETS: THE RELATION BETWEEN POSITIVE LEBESGUE MEASURE AND NON-EMPTY INTERIOR

Qi-Rong Deng () and Si-Min Li
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Qi-Rong Deng: Department of Mathematics, Fujian Key Laboratory of Mathematical Analysis and Applications (FJKLMAA) & Center for Applied Mathematics of Fujian Province (FJNU), Fujian Normal University, Fuzhou, Fujian Province 350117, P. R. China
Si-Min Li: Department of Mathematics, Fujian Key Laboratory of Mathematical Analysis and Applications (FJKLMAA) & Center for Applied Mathematics of Fujian Province (FJNU), Fujian Normal University, Fuzhou, Fujian Province 350117, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 06, 1-7

Abstract: For the self-affine IFS {A−1(x + d i),i = 1,…,m} satisfying the weak separation condition (WSC), let K be the corresponding self-affine set. It is proven in this paper that K has positive Lebesgue measure only if the interior of K is non-empty.

Keywords: Self-Affine Sets; Positive Lebesgue Measure; Non-Empty Interior (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501607

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