Let $f\in C^\infty(\mathbb R;\mathbb R)$ and let us define $g(x)=\vert f(x)\vert$. It is easy to verify that $g$ is locally Lipschitz-continuous function, but I would like to find an example where $g''$ is a distribution with positive order, that is a distribution which not a Radon measure.

Let $f\in C^\infty(\mathbb R;\mathbb R)$ and let us define $g(x)=\vert f(x)\vert$. It is easy to verify that $g$ is locally Lipschitz-continuous function, but I would like to find an example of a smooth function $f$ where $g''$ is a distribution with positive order, that is a distribution which not a Radon measure.

Let $f\in C^\infty(\mathbb R;\mathbb R)$ and let us define $g(x)=\vert f(x)\vert$. It is easy to verify that $g$ is a Lipschitz-continuous function, but I would like to find an example where $g''$ is a distribution with positive order.

Let $f\in C^\infty(\mathbb R;\mathbb R)$ and let us define $g(x)=\vert f(x)\vert$. It is easy to verify that $g$ is locally Lipschitz-continuous function, but I would like to find an example where $g''$ is a distribution with positive order, that is a distribution which not a Radon measure.