The consideration of discontinuous test functions allows us to define the operations of integration of distributions and multiplication of distributions by discontinuous functions which are continuous ...

This example illustrates some properties of splines. Splines are curves, which are usually required to be continuous and smooth. Splines are usually defined as piecewise polynomials of degree n with ...

For nonparametric regression, where the regression function has discontinuity points, the kernel regression estimator and cross-validation are known to be affected by discontinuity.