Confusion about signed Radon measures, Continuous functions and duals

Question

I am studying Radon measures and the duals spaces. There are many slightly different versions of the associated spaces and I am trying to wrap my head around which is related to which space of continuous functions.

Let $X \cong Y$ mean that X is isometric to Y, and denote with $X^\ast$ the dual space of $X$. Consider over $\Omega\subseteq \mathbb{R}^d$ the spaces

• $ba(\Omega)$, space of bounded finitely additive measures
• $rba(\Omega)$, space of regular bounded finitely additive measures
• $\mathcal{M}(\Omega)$ or $rca(\Omega)$, space of regular bounded countably additive measures
• $C_b(\Omega)$, space of bounded continuous funtions
• $C_c(\Omega)$, space of compactly supported continuous funtions
• $C_0(\Omega)$, space of continuous funtions that vanish on the boundary of $\Omega$

Am I right in saying that

1. $C_0(\Omega)\subseteq C_c(\Omega) \subseteq C_b(\Omega)$
2. $rba(\Omega)\cong C_b(\Omega)^\ast$ for arbitrary $\Omega$
3. $rca(\Omega)\cong C_c(\Omega)^\ast$ for compact $\Omega$
4. $rca(\Omega)\cong C_0(\Omega)^\ast$ for arbitrary $\Omega$

Thanks for helping me clarify matters.