= Gaussian interval mass
{title2=$I_\alpha(\theta,b,w)$}
The normalized Gaussian mass of an interval is
$$
I_\alpha(\theta,b,w)=\frac1{\sqrt{4\pi\alpha w}}\int_{-b}^{b}e^{-(\varphi-\theta)^2/(4\alpha w)}d\varphi,\qquad\alpha,w>0.
$$
It is the convolution of an interval indicator with the <heat kernel>, and has an <error function> representation. As the variance tends to zero it converges to the interval indicator away from its endpoints, with value one half at an endpoint. This is a concrete <approximate identity>.
Back to article page
