 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-2/26k/d/solution

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

(X^{2}, η)

, put

A = I \times X

and

B = X \times J

. The marginal conditions give

η (A) = x

and

η (B) = y

, while

A \cap B = I \times J

. The elementary Fréchet inequalities yield

η (A) + η (B) - 1 \leq η (A \cap B) \leq min {η (A), η (B)} .

Hence

x + y - 1 \leq η (I \times J) \leq min {x, y} .

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