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2000•Journal of Mathematical Research and ExpositionRequires access

On the Characterization of the Hausdorff Measure On a Quasi-Self-Similar Set

Su Weiyi

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Abstract

In [1], the characterization of the Hausdorff measure on a self-similar set was given by siegfried GRFA. The concept of quasi-self-similar was introduced by John McLaughin in [2] and then some properties of the Hausdorff measure and dimension on quasi-self-similar sets were disscussed from[3], K. J. Falconer. In this paper, we studied the characterization of the Hausdonff measure on a quasi-self-similar set and deduced that the Hausdorff measure is equavilent to some kind of measure which satisfied some conditions.

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In [1], the characterization of the Hausdorff measure on a self-similar set was given by siegfried GRFA. The concept of quasi-self-similar was introduced by John McLaughin in [2] and then some properties of the Hausdorff measure and dimension on quasi-self-similar sets were disscussed from[3], K. J. Falconer. In this paper, we studied the characterization of the Hausdonff measure on a quasi-self-similar set and deduced that the Hausdorff measure is equavilent to some kind of measure which satisfied some conditions.

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Available abstract

In [1], the characterization of the Hausdorff measure on a self-similar set was given by siegfried GRFA. The concept of quasi-self-similar was introduced by John McLaughin in [2] and then some properties of the Hausdorff measure and dimension on quasi-self-similar sets were disscussed from[3], K. J. Falconer. In this paper, we studied the characterization of the Hausdonff measure on a quasi-self-similar set and deduced that the Hausdorff measure is equavilent to some kind of measure which satisfied some conditions.

Key concepts: Hausdorff measure, Measure (data warehouse), Outer measure, Mathematics, Characterization (materials science), Hausdorff dimension, σ-finite measure, Set (abstract data type)

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