Measure theoretic frameworks for limsup sets

本项目旨在发展新的强大的数学测量理论技术，用于建立解析数论（丢芬图近似）和动力系统中一些不可或缺的结果。计划是建立新技术，并在现有技术不适用的情况下使用它们。由于所提出的框架，我们不仅旨在解决一些长期存在的问题，如广义贝克-施密特问题（1970），而且设想所提出的框架将具有深远的应用，超出丢芬图近似和动力系统的范围，例如，几何测量理论，几何概率和随机几何等。

This project aims to develop new powerful measure theoretic techniques in mathematics that will be used in establishing some indispensable results in analytical number theory (Diophantine approximation) and dynamical systems. The plan is to construct new techniques and to use them in situations where existing techniques are not applicable. As a consequence of the proposed frameworks, not only we aim to resolve a few long-standing problems such as the Generalised Baker-Schmidt Problem (1970) but also envisage that the proposed frameworks will have far-reaching applications beyond the confines of Diophantine approximation and dynamical systems, for example, geometric measure theory, geometric probability and stochastic geometry etc.