Title: Infinite Dimensionality and Measure Theory – Quantum Complexity Metrics

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

This paper investigates the intricate relationship between infinite dimensional spaces and measure theory, focusing on the emergence of "measure-theoretic chaos." We propose a novel method for quantifying the complexity of infinitely dimensional spaces by leveraging the power of measure theory. Specifically, we introduce a new construction that sensitively detects subtle, non-standard configurations, thereby enabling the detection of chaotic behavior within these spaces. The core mechanism centers around capturing statistical properties using measure theory, aiming to provide a robust and quantifiable method for understanding the inherent unpredictability of infinite dimensional spaces. This work seeks to address limitations in existing approaches and offers a potential pathway towards a deeper understanding of quantum complexity metrics.

DOI: 10.5281/zenodo.22598623

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