  We show that Bertini theorems hold for $F$-signature and Hilbert--Kunz
multiplicity. In particular, if $X \subseteq \mathbb{P}^n$ is normal and
quasi-projective with $F$-signature greater than $\lambda$ (respectively the
Hilbert--Kunz multiplicity is less than $\lambda$) at all points $x \in X$,
then for a general hyperplane $H \subseteq \mathbb{P}^n$ the $F$-signature
(respectively Hilbert--Kunz multiplicity) of $X \cap H$ is greater than
$\lambda$ (respectively less than $\lambda$) at all points $x \in X \cap H$.
