Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (2): 293-296.

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The Proof of the Sufficient and Necessary Conditions which Make the Hausdorff Measure of the Generalized Non-uniform Cantor Set'exist

  

  1. College of Mathematics and Information Technology, Hanshan Teacher's College, Chaozhou 521041, China
  • Received:2004-12-25 Online:2006-06-30 Published:2023-12-12
  • About author:ZENG Chao-yi(1958-),male,native of Shaodong,Hunan,an associate professor of Hanshan Teacher's College,engages in fractal geometry.
  • Supported by:
     Supported by the Scientific Research of Hanshan Teacher’s College(2004);

Abstract: The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration (1):Si(x)=aix+bi,x∈[0,1], i=1, 2,…,m, where 0<ai< 1, i=1, 2,…, m; bi+ai>0, i=1, 2,…, m-1, b1=0 and am+bm=1. Providing the sufficient and necessary conditions of its existence Hausdorff measure.

Key words:  , self-similar set, Cantor set, Hausdorff dimension, Hausdorff measure 

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