# Questions tagged [uniform-convergence]

For sequences of functions, uniform convergence is a mode of convergence stronger than pointwise convergence, preserving certain properties such as continuity. This tag should be used with the tag [convergence].

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### Question about applying Dominated Convergence Theorem

Question: $\phi_n(x)=\int_{x_0}^xf(t,\phi_n(t))dt$ ,where $\phi_n(x)$ is continuous on $(a,b)$ and $f$ is continuous and bounded on $(a,b)\times(-\infty,+\infty)$. 1.If $\phi_n(x)$ converges uniformly ...
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### Prove uniform convergence of the series $\frac{(-1)^n}{n+x}$ in $[0,\infty)$

Can it be proved without using dirichlet test for uniform convergence? Edit: Answer is Cauchy Criteria for Uniform Convergence
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### How to prove that this series of functions converges uniformly?

Let $z_0 \in \mathbb{C} \setminus \{0\}$ be a fixed complex number and let $z \in \mathbb{C}$. Let $K \subset \mathbb{C}$ be a compact set. I'm trying to use the Weiertrass $M$ - test to show that the ...
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### the limit of the infimum of a sequence of bounded functions that converge uniformly is equal to the infimum of the limiting function

prove $\lim_{n\to\infty}inf [f_n(x)|x\in E]=inf[f(x)|x\in E]$ where $f_n$ are bounded functions of a set $E\subset R$ that converge uniformly to a function $f$. I've looked at similar proofs on the ...
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