For a document about reinforcement learning, I want to write the joint probability density over the entire trajectory of states and actions like $p(s_0, a_0, s_1, a_1, s_2, ...)$. However, this notation gets quite ugly if you have this more often in a proof. I know from set theory the notation $\{x_i\}_{i=1}^{\infty}$. So would it make sense to write something like $p(\{s_t\}_{t=1}^{\infty}, \{a_t\}_{t=1}^{\infty})$ instead? Or is there another convention? I would like to not come up with something that might just confuse the reader.

Thanks a lot!

For a document about reinforcement learning, I want to write the joint probability density over the entire trajectory of states and actions like $p(s_0, a_0, s_1, a_1, s_2, \dotsc)$. However, this notation gets quite ugly if you have this more often in a proof. I know from set theory the notation $\{x_i\}_{i=1}^{\infty}$. So would it make sense to write something like $p(\{s_t\}_{t=1}^{\infty}, \{a_t\}_{t=1}^{\infty})$ instead? Or is there another convention? I would like to not come up with something that might just confuse the reader.