I am reading a book by one John Conway, and at one point he seems to imply that $\displaystyle \|\chi_{\Delta}\|_2 = \left(\int |\chi_{\Delta}|^2 d \mu\right)^{1/2} = (\mu({\Delta}))^{1/2}$ (where $\displaystyle \chi_{\Delta}$ is the indicator function).

I can't quite understand this. I feel it should just be $\displaystyle \mu({\Delta})$...

So, does anyone know why?

Thanks in advance!