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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 $?