I am reading wikipedia's entry on Holder's inequality https://en.wikipedia.org/wiki/H%C3%B6lder%27s_inequality#Counting_measure
There are quite a few variations of Holder's inequality "applied to different measures" - a phrase quite new to me. I have no idea what this notion of a measure is, when I look up, for example, the counting measure, it says that the counting measure $\nu: S \to [0, \infty]$, is the size of a set $A$. https://www.ma.utexas.edu/users/gordanz/notes/measures.pdf
Can someone please clarify what it means to "apply an inequality to different measures". I am not a mathematician, what is a simple way to understand this idea? Must we specify which measure we are applying an inequality against?