Why order of given distribution is zero?

Question

I was reading the order of distribution.

In-text they provide an example of order zero distribution

I wanted to check my understanding . Please check my argument.

$K\subset \Omega$ be any compact set

$\phi\in D_K$

$|T_{\lambda}\phi|=|\int_K\phi d\lambda|$ $\leq ||\phi||_{\infty}\lambda(K) $

This is true for all K so N=0 here.

Thanks a lot