 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-2/2f/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Yes. Fubini's theorem and the triangle inequality give

d_{1} (T f, T g) \leq \int_{0}^{1} \int_{0}^{1} ∣ K (x, y) ∣ ∣ f (y) - g (y) ∣ d y d x \leq ∥ K ∥_{\infty} d_{1} (f, g) .

Thus $T$ is Lipschitz continuous with respect to $d_{1}$ as well.

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