Course : Mathematical Economics

We formulated an example of application of the ULLN using an iid standard uniform process along with a function space defined on the relevant support that we have already established to be totally bounded wrt the uniform metric. We claimed that the above could be useful in facilitating the convergence in probability of a stochastic minimizer to a limiting deterministic analogue, thereby providing a mathematical structure relevant for the establishment of weak consistency of econometric estimators. 

In order to make sense of the above in our metric space language, we provided a brief reminder of  topological notions in metric spaces with emphasis on the notion of (sequential) convergence and function continuity. Specifying the above in functional speces equipped with the uniform metric we have focused on the notion of uniform functional convergence constrasting it to the (generically non metrizable) notion of pointwise convergence. We will be using this in order to focus on a major application: the approximation of optimization problems.

Notes for the above can be found here and here. The whiteboards from analogous previous year's lectures (please keep in mind that those are not necessarily identical to the current lectures but they contain some common elements) can be found here.