期刊名称：International Journal of Innovative Research in Science, Engineering and Technology
印刷版ISSN：2347-6710
电子版ISSN：2319-8753
出版年度：2016
卷号：5
期号：11
页码：19448
DOI：10.15680/IJIRSET.2016.0511133
出版社：S&S Publications
摘要：In this paper we construct two dimensional Cantor like set S from any sequence { .... } with 0 < ....< 1, Σ.... = ∞ with the help of sequence of sets { .... } of subsets of unit square [0, 1] × [0, 1] such that .... . ........ , S = ∩ ....and m(S) = 0. Two dimensional Cantor ternary set comes out to be a particular case of this construction of twodimensional Cantor like sets by choosing ....= .... for all n. Similarly we can construct two dimensional Cantor like set bychoosing ....= .... for all n, which we have called two dimensional Cantor - .... set, we can construct two dimensionalCantor like set by choosing ....= .... for all n, which we have called two dimensional Cantor - .... set. Also we can constructtwo dimensional Cantor like set by choosing ....= .... for all n, which we have called two dimensional Cantor - .... set.Further we determine the estimates for the Hausdorff dimension of such two dimensional Cantor likesets. In particular it is proved that the Hausdorff dimension of the set S defined above is ≤ .. ........ .... , where .. =lim..→.. log[ Π (.... ....).......... ]...... . In particular ....= .., a constant, 0 < .. < 1, it is proved that the Hausdorff dimension of theset S defined above is ≥ .. ...... ........(........ ).
关键词：Cantor set; Cantor like sets; Hausdorff dimension.
