In positive characteristic the Frobenius endomorphism provides is a powerful and versatile tool for studying singularities. A particular way to use it is by defining singularity measures, i.e., the recipes for assigning a number to a singularity. In my talk, I will define two of such measures, Hilbert-Kunz multiplicity and F-signature, and will study how these measures relate to the natural properties of singularities, for example, under deformations.