Let U be a family of real-valued L-Lipschitz functions on some metric space X. Suppose that there is some real number b and some xo EX such that b ≤ u(xo) for all u EU. Define U: X→ [-∞, +∞] by U(y) = inf{u(y) : u € U}. Show that a) U(X) CR. b) U is L-Lipschitz.

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A: According to our guidelines I can answer only Question no. 4(a).

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