I was reading Poisson structure on $\mathbb{R}^{n}$ , here is the Proposition - "Let {.,.} be a Poisson Structure on $\mathbb{R}^{n}$ .then for any $f,g \in C^{\infty} (\mathbb{R}^{n},\mathbb{R})$" the following relation holds -

$\{f,g\} = \sum_{i,j = 1}^{n} \{x_{i},x_{j}\} \frac{\partial{f}}{\partial_{x_{i}}}\frac{\partial{g}}{\partial_{x_{j}}}$

If any1 could cite a reference that would be extremely helpful! Thank you!

Also posted in Main-

math.stackexchange.com/questions/2174317/a-proposition-on-poisson-structures

Ok,I was dealing with this question asked in main , math.stackexchange.com/questions/2174380/prove-fx-geq-ex

I gave an idea but i think it is wrong but I donot know where ? i think some problem of negation might be there

Got the answer of the problem just asked , problem was with the negation of the statement it is $\exists x < 0$ so I cannot take $x =0$ in my proof !

Anyone know book that connects Fourier Analysis and Measure Theory