Bertini Theorems for $F$-signature and Hilbert-Kunz multiplicity

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 $x\in X\cap H$.