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 Jan 30 answered Feynman lectures, Volume I, chapter 13-4 Jan 18 awarded Yearling Sep 24 comment Example of an additive but not linear map beetween real topological linear spaces Hi, the notation $\mathbb Q [\sqrt {2}]$ stands for the rational multiples of the equivalence class “$\sqrt 2$”, is that right? Moreover, is the point that $f(\sqrt 2 x)=-\sqrt 2 f(x)$ for real $x$? Sep 24 comment Example of an additive but not linear map beetween real topological linear spaces @IttayWeiss altough my knowledge of infinite dimensional vector spaces is very restricted, yes. Sep 24 asked Example of an additive but not linear map beetween real topological linear spaces Sep 14 comment Integrate and measure problem. However, I think that the first version of the post (before I started to confuse things up) was the right one: the integral on $|f|\leq 1$ must be evaluated via the monotone convergence theorem (negating before and after the integral, and defining $-\log 0=\infty$): this is so because the hypothesis of the DCT, that is, that the pointwise limit is a complex measurable function, is not met where $f(x)=0$, and this set could have positive measure. Sep 14 comment Integrate and measure problem. Hi robjohn, thank you. I understand the point, on $|f|\leq 1$ the pointwise limit of $g_p(f)$ isn't necessarily a complex measurable function (if $f(x)=0$). Sep 13 comment Integrate and measure problem. Sorry, I meant the $p_0$ of the OP. Sep 13 comment Integrate and measure problem. Hi robjohn, do we really need to split the integral in two parts, in in (2f)? It looks to me that we can apply dominated convergence to the whole integral, using $g_r(|f|)$. Aug 18 awarded Popular Question Jun 25 comment Is the Cauchy-Schwarz inequality ever used in Physics? That's the perfect example! See, for instance, Sakurai “Modern Quantum Mechanics”, 1.4 . Apr 15 comment How to estimate the axis of symmetry for an even function with error? You are welcome! If the large error is on the $y_i$'s, I've added a second (maybe more practical) method that could work. Apr 15 revised How to estimate the axis of symmetry for an even function with error? added 671 characters in body Apr 15 answered How to estimate the axis of symmetry for an even function with error? Apr 8 awarded Enlightened Apr 7 awarded Nice Answer Mar 5 answered Show that $A =\left(\begin{smallmatrix}41&12\\12&34\end{smallmatrix}\right)$ is symmetric positive definite Mar 4 comment Show that $A =\left(\begin{smallmatrix}41&12\\12&34\end{smallmatrix}\right)$ is symmetric positive definite Hint for alternative method: is there any relationship beetween $A$'s eigenvalues and quantities like, for example $\det A$? Jan 31 accepted Differential of the inversion of Lie group Jan 22 awarded Peer Pressure