A study on Quantization Dimension in complete metric spaces

2020/05/16 by Mrinal Kanti Roychowdhury, Roychowdhury, Mrinal K., Saurabh Verma +1
Decision Sciences · Mathematics · #28A80 #37A50 #60D05 #94A15 #Dynamical Systems (math.DS) #FOS: Mathematics #Fixed Point Theorems Analysis #Fuzzy and Soft Set Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2005.07840

openalex publication_date 2020/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a complete metric space. This generalizes the known results on quantization dimension of self-similar measures in the Euclidean space to a complete metric space. In the last part, continuity of quantization dimension is discussed.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

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