Definition

A deterministic Markov control policy $\gamma\in\Gamma_{M}$ is a sequence of functions $\{ \gamma_{t} \}$ s.t. $$\gamma_{t}:\mathbb{X}\times \mathbb{Z}_{+}\to \mathbb{U}$$and $$u_{t}=\gamma_{t}(x_{t})$$$\forall t\in\mathbb{Z}_{+}$.