I hope I will be forgiven for having such a basic question. I am trying to understand Definition 1.21 of Meng. I paste the definition here:
I assume this can be written with more traditional notation as $-\text{log } \text{sup }S$ for some subset $S.$ But what should $S$ be ?
Meng's definition is not rigorously formulated because of his $\exists$ before $t$. My guess is that he meant $$-\log\sup\{t\in[0,1]\mid\exists c\in C,\;a=tb+(1-t)c\}.$$