Each f_n is bounded (by n) on [0,1], the sequence f_n converges pointwise to f on ]0,1], but f is not bounded on ]0,1].
Boundedness is not preserved by pointwise convergence.
Each f_n is bounded (by n) on [0,1], the sequence f_n converges pointwise to f on ]0,1], but f is not bounded on ]0,1]. [br]This counter-example shows that pointwise convergence does not, in general, preserve boundedness.
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