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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?