The purpose of this chapter is to show that Lebesgue measurable sets are well approximated by open sets and by closed sets. Of course we have to specify the sense or the topology in which these approximations take place. Figure 11.1 Approximation from the outside by an open set. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351056823/5c92c9a4-ddd5-4d42-82bc-8e5903ddaaca/content/fig11_1.tif"/>