The Contraction Method on C([0,1]) and Donsker's ... - Eurandom
The Contraction Method on C([0,1]) and Donsker's ... - Eurandom
The Contraction Method on C([0,1]) and Donsker's ... - Eurandom
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For µ, ν ∈ M1(R) let<br />
<str<strong>on</strong>g>C<strong>on</strong>tracti<strong>on</strong></str<strong>on</strong>g><br />
ℓ1(µ, ν) = inf E[|X − Y |]<br />
X ,Y :L(X )=µ,L(Y )=ν<br />
ℓ1 is a complete metric <strong>on</strong> M1(R) <strong>and</strong><br />
ℓ1(µn, µ) → 0 ⇒ µn w → µ.<br />
Show: F is a c<strong>on</strong>tracti<strong>on</strong> according to ℓ1 in M1(R).<br />
Henning Sulzbach J. W. Goethe-Universität Frankfurt a. M. <str<strong>on</strong>g>The</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>tracti<strong>on</strong></str<strong>on</strong>g> <str<strong>on</strong>g>Method</str<strong>on</strong>g> <strong>on</strong> C([0, 1]) <strong>and</strong> D<strong>on</strong>sker’s <str<strong>on</strong>g>The</str<strong>on</strong>g>orem