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 Nov 25 comment Exchanging Series with Integrals: when is it possible? Note that by linearity, it's always possible to do this for finite sums. For infinite sums, it becomes a matter of exchanging a limit and an integral which you can use Fubini's convergence theorem, monotone convergence theorem, Vitali's convergence theorem, etc. Nov 25 comment Convergence of $\sum_{-\infty}^{\infty}e^{-\pi tn^2}$ Thank you very much. I had an inkling that it was this simple. Nov 25 accepted Convergence of $\sum_{-\infty}^{\infty}e^{-\pi tn^2}$ Nov 25 asked Convergence of $\sum_{-\infty}^{\infty}e^{-\pi tn^2}$ Sep 28 awarded Popular Question Sep 7 awarded Notable Question Jul 6 comment Prove that $V$ is the direct sum of $W_1, W_2 ,\dots , W_k$ if and only if $\dim(V) = \sum_{i=1}^k \dim W_i$ I think you mean the sum of the dimension of the span of $B_i$ is the dimension of $W_i$. Jul 4 comment Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$. My question would be if this proof is correct. I saw this problem in an old analysis book and so I thought I would try it out. Sorry, I should have been more clear. Jul 4 revised Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$. added 148 characters in body Jul 4 comment Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$. Sorry about that, I have corrected the statement in my edit. Jul 4 revised Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$. added 98 characters in body Jul 4 asked Let $f=g$ on $[a,b]/E$ where $f\in \mathcal{R}[a,b]$ and continuous on $[a,b]$. Then $g\in\mathcal{R}[a,b]$ and $\displaystyle\int_a^b f=\int_a^bg$. Jun 19 accepted If, $\lim x_n$ exists and finite then there is a function $f$ that is continuous Jun 19 asked If, $\lim x_n$ exists and finite then there is a function $f$ that is continuous Jun 6 accepted Difficult limits every grad should be able to do Jun 5 asked Difficult limits every grad should be able to do May 27 accepted $\lim_{n\to \infty} n^{1/n^2}$ May 27 comment $\lim_{n\to \infty} n^{1/n^2}$ Ahh, this is much better. Thanks! May 27 asked $\lim_{n\to \infty} n^{1/n^2}$ May 26 comment Bounded sequence of positive numbers Do you mean $r$ instead of $K$?