Yuqin Zhang
Abstract
In this article,we show that:the self-similar measure is either singular or absolutely continuous with respect to Lebesgue measure and the converse is true when Lebesgue measure is restricted to the compact support of the self-similar measure, which generalizes the result of Yuval Peres, etc., see[1].
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
In this article,we show that:the self-similar measure is either singular or absolutely continuous with respect to Lebesgue measure and the converse is true when Lebesgue measure is restricted to the compact support of the self-similar measure, which generalizes the result of Yuval Peres, etc., see[1].
Key concepts: Mathematics, Lebesgue–Stieltjes integration, σ-finite measure, Lebesgue measure, Measure (data warehouse), Converse, Absolute continuity, Lebesgue's number lemma