Young Measures on Topological Spaces: With Applications in Control Theory and Probability Theory

By C. Castaing, P. R. D. Fitte, M. Valadier. 2004

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New dependence coefficients. Examples and applications to statistics (2005, methodology): “Using the equality (3.4.4) in Castaing et al. (2004) instead of Proposition 1.2 in Dedecker and Prieur (2004), we see that (7.5) is true for any σ-agebra M of A and any continuous distance d0 with respect to d.”
Characterization of Generalized Gradient Young Measures Generated by Sequences in W1,1 and BV (2010, background): “After Young’s original papers [57–59], many have contributed to this theory, note in particular [9, 12, 13, 17, 41, 42, 56] as well as the books [20, 51, 53] and the references cited therein.”
Mean field games with common noise (2014, unknown): “ric spaces and µ∈ P(E). If µis nonatomic, then the set µ(dx)δφ(x)(dy) ∈ P(E×F) : φ: E→ F is continuous is dense in P(E,µ;F) := {P∈ P(E×F) : P(· ×F) = µ}. Proof. This would be exactly Theorem 2.2.3 of [13], if we replaced the word “continuous” with “measurable.” Our result follows simply by noting th”