en.wikipedia.org/wiki/AIXI

In the AIXI literature, a deterministic policy maps a history directly to an action. That is exactly the type signature shown here: π : (A × E)* → A.

Primary sources describe it this way:

• Veness et al. state: "Formally, a policy is a function that maps a history to an action" and then write π:(A×X)*→A.
• An official AIXI overview on Hutter's site distinguishes the two cases explicitly: in general a stochastic policy is a distribution over actions, π:(A×E)*→ΔA, while the Bayes-optimal/AIXI-style policy is deterministic.

So the article's sentence is internally inconsistent: it calls π a stochastic policy while simultaneously giving the type of a deterministic policy.

This type signature is incorrect for a stochastic environment.

Earlier in the article, the environment is correctly described as a probability distribution over percepts conditioned on the history and next action. For that reason, its codomain cannot be E itself; it must be a space of probability measures over E.

Primary sources define the environment that way:

• The official AIXI overview on Hutter's site writes the environment as a distribution over percepts with type ν:(A×E)*×A→ΔE.
• Veness et al. define an environment as a sequence of conditional probability functions and call it a probability distribution over possible observation-reward sequences conditioned on actions.

So writing μ : (A × E)* × A → E is mathematically wrong for the stochastic AIXI setting. That type would describe a deterministic environment, not the probability distribution the text is discussing.