SOLVED:Prove or give a counterexample: if U is a subspace of V that is invariant under every operator on V, then U={0} or U=V.

SOLVED:Prove or give a counterexample: If ft: 𝐑 →𝐑 is a Borel measurable function for each t ∈𝐑 and f: 𝐑 →(-∞, ∞] is defined by f(x)=sup{ft(x): t ∈𝐑} then f is a Borel measurable function.

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Which of the following statments are true, and which are false?... | Filo