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Corollary: Every uniformly convergent sequence of functions is pointwise convergent.

(related to Definition: Pointwise and Uniform Convergence)

If a sequence of functions \((f_n)_{n\in\mathbb N}\) converges uniformly to a function \(f\), then it also converges pointwise to \(f\).

Table of Contents

Proofs: 1

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
2. Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984