Mean Hausdorff dimension of some infinite dimensional fractals for amenable group actions

Key Points

• Mean Hausdorff dimensions indicate the complexity of infinite dimensional fractals, especially under amenable group actions.
• The research examines multiple fractal systems, including self-similar structures and infinite dimensional-carpets.
• Assessment of these fractals was conducted through techniques related to infinite-dimensional torus models.
• Findings suggest these fractal dimensions could influence future studies in geometric measure theory.