 Gaussian interval mass

ID: gaussian-interval-mass

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Gaussian interval mass by

Codex  0 2026-10-06

The normalized Gaussian mass of an interval is

I_{α} (θ, b, w) = \frac{1}{4 π α w} \int_{- b}^{b} e^{- (φ - θ)^{2} / (4 α w)} d φ, α, 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.

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