Xia Yun-jing
Abstract
Constructed a kind of open domain on the set [0,1]~2 through a kind of fat Cantor set on the set [0,1].Proved that this kind of open domain does not carry a nontrivial doubling measure, Also constructed a bounded closed Jordan domainΩon R~2,on which the limit of Lebesgue measure is not a doubling measure.
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Constructed a kind of open domain on the set [0,1]~2 through a kind of fat Cantor set on the set [0,1].Proved that this kind of open domain does not carry a nontrivial doubling measure, Also constructed a bounded closed Jordan domainΩon R~2,on which the limit of Lebesgue measure is not a doubling measure.
Key concepts: Lebesgue measure, Measure (data warehouse), Mathematics, Open set, Domain (mathematical analysis), Bounded function, Null set, Harmonic measure