$\lim_{n \to \infty} \mu(x| |f_n-f|>\frac{1}{n})=0$ what kind of convergence is this? What does this say about $f_n \to f$?

Question

$$\lim_{n \to \infty} \mu(x| |f_n-f|>\frac{1}{n})=0$$

I was asked a question on whether this implies convergence in measure. I proved that it does by monotonicity of measures. Thus $f_n\to f$ in measure. Can something more be said? We can assume that $\mu$ is the lebesgue measure if it implies something more interesting.

Thank you.