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Apr
11
comment Exercise #9 in chapter 11 of Rudin's Principles of Mathematical Analysis.
@Minus22 It is just the characteristic function of the set $[x_n,x]$, that is $\mathbf{1}_{[x_n,x]}(t)=1$ if $t\in [x_n,x]$ and $0$ otherwise.
Apr
11
answered Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$
Apr
11
answered Exercise #9 in chapter 11 of Rudin's Principles of Mathematical Analysis.
Apr
10
revised Show that $L^1$ function is $0$ a. e.
title
Apr
10
answered Show that $L^1$ function is $0$ a. e.
Apr
4
answered If $z_{n} \rightarrow z$ then $|z_{n}|\leq M$ for all n.
Apr
4
awarded  sequences-and-series
Apr
3
revised $n$-sphere is smooth manifold
deleted 11 characters in body
Apr
3
revised $n$-sphere is smooth manifold
fixed grammar, spelling
Apr
3
revised Convergence in distributions
fixed title, grammar
Apr
3
revised Proof of lemma in order to prove Cauchy-Schwarz inequality
fixed formatting, grammar
Apr
3
answered Proof of lemma in order to prove Cauchy-Schwarz inequality
Apr
3
answered Convergence in distributions
Mar
29
comment Notation in harmonic analysis
$x\in\mathbb{R}^n$, @AkivaWeinberger
Mar
29
answered Notation in harmonic analysis
Mar
27
revised Proof that $\|S_N\|_p < \infty $ is equivalent to $\|S_N f - f\|_p \to 0$ as $N \to \infty$
minor typos
Mar
27
answered Measure of “subspace”, has it a sense?
Mar
27
answered Proof that $\|S_N\|_p < \infty $ is equivalent to $\|S_N f - f\|_p \to 0$ as $N \to \infty$
Mar
27
comment Proof that $\|S_N\|_p < \infty $ is equivalent to $\|S_N f - f\|_p \to 0$ as $N \to \infty$
But that equality implies $f_\ell=S_{N_\ell} f_\ell$ which is impossible by choice of $f_\ell$.
Mar
26
comment Show that $\sqrt{2}$ is an irrational number with strong mathematical induction
What is strong induction? Is there a weak induction too?