Duality on Banach spaces and a Borel parametrized version of Zippin's theorem

Let SB be the standard coding for separable Banach spaces as subspaces of $C(\Delta)$. In these notes, we show that if $\mathbb{B} \subset \text{SB}$ is a Borel subset of spaces with separable dual, then the assignment $X \mapsto X^*$ can be realized by a Borel function $\mathbb{B}\to \text{SB}$. Moreover, this assignment can be done in such a way that the functional evaluation is still well defined (Theorem $1$). Also, we prove a Borel parametrized version of Zippin's theorem, i.e., we prove that there exists $Z \in \text{SB}$ and a Borel function that assigns for each $X \in \mathbb{B}$ an isomorphic copy of $X$ inside of $Z$ (Theorem $5$)

Growth, Fiscal Policy and the Informal Sector in a Small Open Economy

We discuss the implications of informality on growth and fiscal policy by considering an informal sector based on low tech firms, in an open economy model of endogenous growth, where labour supply is elastic and increasing returns arise from public spending. We allow for both labour and capital to allocate between sectors and examine the dynamic and policy issues that arise in an economy, where long run outcomes are still dominated by formal activities, but long macroeconomic transitions arise as a result of informal microeconomic activities, which take advantage of both government taxation and limited fiscalization.Endogenous Growth Theory; Optimal Fiscal Policy; Informal Sector; Public Capital