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Given a function sequence f1(x), f2(x), f3(x)..., the limit can be defined in several ways:
- Point by point limit; that is, it converges to a new function at each point.
- Lp convergence; that is, it converges to a new function in Lp-norm.
- Almost everywhere convergent; that is, it converges to a new function except a set with measure zero.
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