What question did this study set out to answer?

To develop a unified approach to measure convergence rates towards points at infinity in various mathematical spaces.

December 19, 2025Open Access

Measuring Asymptotic Convergence: A Unified Framework from Isotropic Infinity to Anisotropic Ends

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To develop a unified approach to measure convergence rates towards points at infinity in various mathematical spaces.
Defined a point at infinity for arbitrary spaces via exhaustion functions.
Introduced parameterized norms for quantifying convergence rates.
Developed a multi-exhaustion formalism for anisotropic spaces.
The framework distinguishes between global convergence and asymptotic behavior at infinity.
Provided sufficient conditions for convergence based on monotonicity.
Illustrated practical examples demonstrating the concepts across different spaces.

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This framework measures convergence rates in metric and topological spaces, indicating deeper asymptotic behavior analysis.

Arshak Petrosyan (2025) studied this question.

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