Fatou's lemma and monotone convergence theorem

In this post, we deduce Fatou's lemma and monotone convergence theorem (MCT) from each other.

Young's, Hölder's and Minkowski's Inequalities

In this post, we prove Young's, Holder's and Minkowski's inequalities with full details. We prove Hölder's inequality using Young's inequality. Then we prove Minkowski's inequality by using Hölder.