# Tagged Questions

Convergence of sequences and different modes of convergence.

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### Convergence of minimum of a sequence of functions

Consider functions $f_n, f$ from $\mathbb{R}$ to $\mathbb{R}$. Suppose $f_n(y)$ converges pointwise to $f(y)$ for all $y$ as $n \rightarrow \infty$. I would like to know under what conditions is the ...
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### Convergence of integral $\int_{0.5}^{1} \log(|\log(t)|)\ ^ 7\,\mathrm{d}t$

Does this integral converge ? $$\int_{0.5}^{1} \log(|\log(t)|)\ ^ 7 \,\mathrm{d}t$$ I have tried to compare this integral to $$\int_{0.5}^{1} \dfrac{1 }{\sqrt{x-1}} \,\mathrm{d}t$$ but couldn't ...
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### Summary of results concerning interchange of limits in series

The document http://www2.iugaza.edu.ps/ar/periodical/articles/volume%2014-%20Issue%201%20-studies%20-16.pdf constructs the theory of double sequences and double series very nicely, supplying the ...
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### Confusion about the convergence of Riemann zeta function in terms of the integral

Titchmarsh wrote that $$\zeta(s)=s\int_{1}^{\infty}\frac{\left \lfloor x \right \rfloor-x+\frac{1}{2}}{x^{s+1}}\,\mathrm{d}x+\frac{1}{s-1}+\frac{1}{2}\tag{2.14}$$ using the Euler-Maclaurin summation, ...
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### Revision of Borel-Cantelli, $(X_n)_{n \geq 1}$ sqn of $\geq 0$ identical RVs with $E(X) < \infty$ then $X_n/n \to 0$ a.s., are my arguments correct?
Let $A = C_r^*(S_\infty)$ where $S_\infty$ - is permutation group of natural numbers fixing all but a finite number of element. Let $A_n = C_r^*(S_n)$ - subspaces of $A$ and $P_n : A \to A$ is ...