I'm working on understanding a textbook on Mechanism Design and I came across a part that I didn't quite understand, which is underlined in RED:
What does the underlined part refer to? I know it's an interval of some sort, but I'm clueless beyond that.
Interval Notation is a method of specifying a chunk of the real numbers using the endpoint values and brackets of varying types to say what the nature of that end point is. In this case, $[\theta_i,\overline {\theta_i} \cdot \overline {m_i}]$ means all the numbers between $\theta_i$ and $\overline {\theta_i} \cdot \overline {m_i}$, including both endpoints.