Mathematical Economics

We begun with an equivalent definition that is useful for the introduction of total boundness. Strenghtening thus, the boundedness characterization we have introduced the notion of total boundness. We have started  our examination of the latter. We have given properties, e.g. that the centers of the covering balls can be chosen inside the totally bounded set, as well as (trivial) examples-counterexamples (the analytical complexity of the notion clearly manifested itself on that counter examples were easier to come up to).

Given the analytical complexity of the verification of total boundness, we will use the introduction of the notions of covering numbers and metric entropy in order to construct examples and further properties. We left this pending for the following lecture.

We have instead begun the investigation of an application of the notion of total boundedness in asymptotic analysis, by deriving a Uniform Law of Large Numbers in a simple framework.

Notes on the above can be found  here, and here.  Notes on the ULLN application can be found here.  

The whiteboards from analogous academic year's 2020-21 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, and here.