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Florian, Gunsilius. (2021) Distributional synthetic controls.
In: Papers. RePEc:arx:papers:2001.06118.
Full description at Econpapers
cites:
A Proofs Before turning to the proofs, we need to introduce notation. Following Agueh & Carlier (2011), we define the space of continuous functions with at most quadratic growth by Cq := (1 + k k2 2)Cb(Rd ) = f ∈ C(Rd ) : f 1 + k k2 is bounded , which will be equipped with the norm kfkq := sup y∈Rd |f(y)| 1 + kyk2 , where k k2 denotes the Euclidean norm in Rd and Cb(Rd ) denotes the space of all bounded and continuous functions. Throughout, we work in the closed subspace Cq,0 of Cq given by Cq,0 := (1 + k k2 2)C0(Rd ) = f ∈ C(Rd ) : lim kyk2→∞ f(y) 1 + kyk2 = 0 ,
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