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

Qi-Rong Deng; Simin Li

doi:10.1142/s0218348x21501607

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

Qi-Rong Deng Simin Li

Year: 2021 Journal: Fractals Vol: 29 (06)Pages: 2150160-2150160 Publisher: World Scientific

DOI: 10.1142/s0218348x21501607

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Abstract

For the self-affine IFS [Formula: see text] satisfying the weak separation condition (WSC), let [Formula: see text] be the corresponding self-affine set. It is proven in this paper that [Formula: see text] has positive Lebesgue measure only if the interior of [Formula: see text] is non-empty.

Keywords:

Affine transformation Mathematics Lebesgue measure Measure (data warehouse) Lebesgue integration Set (abstract data type) Relation (database) Pure mathematics Computer science

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Mathematical Dynamics and Fractals

Physical Sciences → Mathematics → Mathematical Physics

Advanced Topology and Set Theory

Physical Sciences → Mathematics → Geometry and Topology

Advanced Differential Equations and Dynamical Systems

Physical Sciences → Mathematics → Geometry and Topology

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

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