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.
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8$\begingroup$ It could be helpful to adopt a convention like $\mathbf{s}=\{s_t\}_{t=1}^{\infty}$ and then write $p(\mathbf{s},\mathbf{a})$. Or $\vec{s}$ is another notation I've seen used for this purpose (representing a tuple). $\endgroup$– Sam HopkinsCommented Nov 13, 2021 at 20:35
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