We present a theoretical study of signed measures, complex measures and vector measures. The study is focused on the Radon-Nikodym Theorem and the Riesz representation Theorem (its various versions). Complex Radon measures over locally compact Hausdorff spaces are extensively treated. Regarding vector measures, we aim to provide a vision deep enough on Bochner integration to prove that vector extensions of the latter theorems are not generally true and to discuss when they are.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: María Jesús Carro Rossell