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Apr
25
awarded  Popular Question
Apr
12
comment Prove that $K$ is compact
$l^\infty$ is a normed space (metric space is enough), so compactness of $K$ is equivalent to the statement that every sequence in $K$ has a subsequence which converges to an element of $K$.
Apr
12
answered Prove that $K$ is compact
Apr
10
comment Proving that $f = 0$ if $\int fg = 0$ for all $g \in S$
@MehdiJafarniaJahromi This is dominated convergence. For a fixed Schwartz $g$, $g$ is bounded, and we may assume the $a_n$ are uniformly bounded above by $1$, so the whole thing is dominated by $|f|$.
Apr
10
answered Proving that $f = 0$ if $\int fg = 0$ for all $g \in S$
Apr
9
answered f bounded by an integrable function implies f is measurable
Apr
4
awarded  Notable Question
Mar
30
comment Show that $g$ is increasing over $I$
I mention it because if your interval $I$ is of the form $[a,0]$ then it does not contain any nontrivial interval of the form $[0,b]$, so the first part doesn't apply.
Mar
30
comment Show that $g$ is increasing over $I$
In the case that your interval contains an interval of the form $[a,0]$, consider instead $[0,|a|]$ to get $x\in(0,|a|]$ and $h>0$ with $g(x+h) < g(x)$. But then since $g$ is odd we now have $-g(-x-h) < -g(-x)$ so that $g(-x) < g(-x-h)$ and again we find that $g$ is not increasing on $[a,0]$.
Mar
30
comment Show that $g$ is increasing over $I$
Any nontrivial interval containing $0$ contains a smaller interval of the form $[0,b]$ or $[a,0]$ which is nontrivial. If $f$ isn't increasing on $[0,b]$, it will not be increasing on any bigger interval either.
Mar
30
answered Show that $g$ is increasing over $I$
Mar
30
awarded  Nice Question
Mar
29
answered What is the difference between two function spaces
Mar
29
answered The squeeze theorem in the sequence $u_n=(\frac{2n}{3n+1})^n$, $n \in \Bbb{Z^+}$
Mar
29
reviewed Leave Open Is $d(x,y)=|x-y|^2$ a distance on $\mathbb{R}$?
Mar
29
reviewed Close Can every function be represented as polynomial
Mar
29
reviewed Close optimization problem :using probability dynamic programming
Mar
29
reviewed Leave Open Numerical derivative of function wrt natural log of variable (non-analytic)
Mar
29
reviewed Leave Open How to count in 4 dimensions an infinite set of 3rd degree polynomials (with integer coefficients a,b,c,d) using Cantors diagonilaziation?
Mar
29
comment Absolute continuity on limit
Edited so you can correct your vote, thank you.