(a) If Uk) is a bounded sequence in M[a, b] and ik ~ i a.e., show that i E M[a, b]
Chapter 10, Problem 14(choose chapter or problem)
(a) If Uk) is a bounded sequence in M[a, b] and ik ~ i a.e., show that i E M[a, b]. [Hint:Use the Dominated Convergence Theorem.](b) If (gk) is any sequence in M[a, b] and if ik := Arctan 0 gk' show that Uk) is a boundedsequence in M[a, b].(c) If (gk)is a sequencein M[a, b] andif gk ~ g a.e.,showthatg E M[a, b].
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