Convergence of random variables

2019-12-02 — 2019-12-02

Wherein the distinctions between modes of convergence are examined, and the absence of any metric for almost-sure convergence on probability spaces is highlighted, while metrizable notions such as convergence in distribution and in Lp are contrasted.

Figure 1

Placeholder. When does one random variable approach another? There are many ways we could define this concept and various interesting relationships between these ways.

Djalil Chafaï, About convergence of random variables.

To discuss: metrics versus types of convergences. The magical world of a.s. convergence which has no metric. The role of probability spaces.