I am reading LS book "Recursive Macroeconomics Theory".
In this book, as well as in some online lecture notes on the Internet. They often denote, for example, $\pi_t(s^t)$ for probability that history $s^t$ happens at time $t$.
But I wonder, if we are mentioning $s^t$, it implies time is $t$. So, why don't we just make it simple by writing $\pi(s^t)$ instead?
Thank in advance for any help!