3 papers
math.DS2026
Some remarks on the exponential separation and dimension preserving approximation for sets and measures
Saurabh Verma, Ekta Agrawal, Megala M
In the dimension theory of sets and measures, a recent breakthrough happened due to Hochman, who introduced the exponential separation condition (ESC) and proved the Hausdorff dime…
math.DS2025
Some results on Lower Assouad and quantization dimensions
Saurabh Verma, Ekta Agrawal, Shivam Dubey
In this paper, we first show that the collection of all subsets of \( \mathbb{R} \) having lower dimension \( γ\in [0,1] \) is dense in \( Î (\mathbb{R}) \), the space of compact…
math.DS2025
Dimension preserving set-valued approximation and decomposition via metric sum
Ekta Agrawal, Saurabh Verma
In the literature, the Minkowski-sum and the metric-sum of compact sets are highlighted. While the first is associative, the latter is not. But the major drawback of the Minkowski…