Introduction to Lp Spaces: Hölder's inequality, Minkowski inequality

In this video, we will define Lp spaces for measure spaces. In order to prove that the p-norms are norms, we are going to derive Hölder's inequality with Young's inequality and then show the Minkowski inequality. 00:00 Motivation in n-dimensional space 02:58 Definition of p-norms 05:05 Young's inequality 06:10 Hölder's inequality 07:05 Minkowski inequality 07:18 Construction of Lp spaces 08:36 Properties of Lp spaces