# Questions tagged [pointwise-convergence]

For questions about pointwise convergence, a common mode of convergence in which a sequence of functions converges to a particular function. This tag should be used with the tag [convergence].

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### Point-wise convergence of $f_{n,m}(x) = \cos^{2n}(m!)\pi x$

I have recently been trying some questions on convergence of sequence of functions.I got stuck in one of the problems in which I am supposed to find the point-wise limit and discuss the uniform ...
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### Uniform convergence of sequence of functions $\frac{2+nx^2}{2+nx}$ on [0,1]?

I have recently been trying some questions related to the uniform convergence of a sequence of functions. And meanwhile, I got stuck in one of the problems in which I have been supposed to discuss the ...
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### True or False: convergence on L1 of a martingale Xn with E|Xn|=1

I have to prove whether the next statement is true or not: 'if {Xn} for n>=1 to infinitive it is such a martingale that for everything n>=1, Xn>=0 and E|Xn|=1, then the sequence {Xn} for n>=1 to ...
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### Prove Uniform Convergence for $\{f_n\}$ [duplicate]

Suppose $\{f_n\}$ is an equicontinuous sequence of functions defined on $[0,1]$ and $\{f_n(r)\}$ converges $∀r ∈ \mathbb{Q} ∩ [0, 1]$. Prove that {$f_n$} converges uniformly on $[0, 1]$. There are ...
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### Sequence of continuous fuctions with compact support converges to 1.

Let $X\subset\mathbb{R}^d$ be an unbounded closed set and $C_0$ is the space of all continuous functions $h: X\to \mathbb{R}$ with compact support. I'm searching for the sequence \$\{ h_n \} \subset ...
I'm given a function sequence as such: $$f_n(x) = \frac{x^n}{n^n}$$ over $$x \in [0,1]$$ I have to find what is the point convergence and uniform convergence of this sequence. What is the proper ...