Noetherian ring/Positive characteristic/Existence of Hilbert-Kunz multiplicity/Fact

Existence of Hilbert-Kunz multiplicity

Let ${}K$ denote a field of positive characteristic ${}p$, let ${}K\subseteq R$ be a noetherian ring and let ${}I\subseteq R$ be an ideal which is primary to some maximal ideal.

Then the Hilbert-Kunz multiplicity ${}e_{HK}(I)$ exists and is a positive real number.

Write a proof