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RESEARCH PRODUCT

The arithmetic decomposition of central Cantor sets

Francesco TuloneFranciszek Prus-wiśniowski

subject

Class (set theory)Mathematics::Dynamical SystemsLebesgue measureApplied Mathematics010102 general mathematicsZero (complex analysis)Analysi02 engineering and technology01 natural sciencesCentral Cantor setCantor setCombinatoricsSet (abstract data type)Arithmetic progression0202 electrical engineering electronic engineering information engineeringDecomposition (computer science)Palis hypothesiArithmetic decomposition020201 artificial intelligence & image processing0101 mathematicsComputer Science::DatabasesAnalysisMathematics

description

Abstract Every central Cantor set of positive Lebesgue measure is the arithmetic sum of two central Cantor sets of Lebesgue measure zero. Under some mild condition this result can be strengthened by stating that the summands can be chosen to be C s regular if the initial set is of this class.

yearjournalcountryeditionlanguage
2018-11-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2018.05.065