Preface -- 1 Weak Compactness in Measure Spaces -- 1.1 Measure Spaces -- 1.2 Radon-Nikodym Theorem. The Dual of L1 -- 1.3 Convergences in L1(λ) and ca(A) -- 1.4 Weak Compactness in ca(A) and L1(λ) -- 1.5 The Bidual of L1 (λ) -- 1.6 Extensions of Dunford-Pettis' Theorem -- 2 Bounded Measures on Topological Spaces -- 2.1 Regular Measures -- 2.2 Polish Spaces. Suslin Spaces -- 2.3 Narrow Topology -- 2.4 Compactness Results -- 2.5 Metrics on the Space (Rca+(ℬT), T) -- 2.5.1 Dudley's Metric -- 2.5.2 Lévy-Prohorov's Metric -- 2.6 Wiener Measure -- 3 Young Measures -- 3.1 Preliminaries -- 3.1.1 Disintegration -- 3.1.2 Integrands -- 3.2 Definitions and Examples -- 3.2.1 Young Measure Associated to a Probability -- 3.2.2 Young Measure Associated to a Measurable Mapping -- 3.3 The Stable Topology -- 3.4 The Subspace ℳ(S) ⊆ Y(S) -- 3.5 Compactness -- 3.6 Biting Lemma -- 3.7 Product of Young Measures -- 3.7.1 Fiber Product -- 3.7.2 Tensor Product -- 3.8 Jordan Finite Tight Sets -- 3.9 Strong Compactness in Lp(µ, E) -- 3.9.1 Visintin-Balder's Theorem -- 3.9.2 Rossi-Savaré's Theorem -- 3.10 Gradient Young Measures -- 3.10.1 Young Measures Generated by Sequences -- 3.10.2 Quasiconvex Functions -- 3.10.3 Lower Semicontinuity -- 3.11 Relaxed Solutions in Variational Calculus -- Bibliography -- Index.