Notation for minimum

Question

I'm reading Huber's Robust Statistics right now, and at the beginning of Chapter 3, he writes the following notation:

$$\sum \rho(x_i;T_n) = \min!$$

Similarly, a few lines down, he writes:

$$\sum \rho(x_i - T_n) = \min!$$

Can someone help me understand what this $\min!$ notation means?

Thanks!

Answer 1

min! is the argmin, i.e., $f(x)=\min!$ is identical to $\arg \min f(x)$.

See also https://mathoverflow.net/questions/182112/a-question-about-some-notation-involving-the-exclamation-mark and the link there, which discusses your example.