Point-Wise Compact Subsets of the First Baire Class

Summary:Let $(A_0, A_1)$ be a regular interpolation couple. Under several different assumptions on a fixed $A^{\beta}$, we show that $A^{\theta} = A_{\theta}$ for every $\theta \in (0, 1)$. We also deal with assumptions on $\overline{A}^{\beta}$, the closure of $A^{\beta}$ in the dual of $(A_0^*, A_1^*)_\beta$