Theorem. Direct utility transport bound [ftip-00G4]
✍️source

    Under Definition [ftip-00G3], every artifact \(M\) satisfies \(|J_s(M)-J_t(M)|\leq \varepsilon \).

    Proof. 

      Pointwise bounds give \(-\varepsilon \leq s_M(z)-t_M(z)\leq \varepsilon \). Taking expectations preserves both inequalities.