What does notation $\inf_{k,l}$ mean for indices $k,l$?

Question

What does notation $\inf_{k,l}$ mean for indices $k,l$?

Does it mean that one picks $\inf k$ and $\inf l$ or that one picks some kind of "inf of both $k$ and $l$" (whatever that means)?

Answer 1

Unless the context clearly explains a different convention I would expect $$ \inf_{k,l} f(k,l) $$ to mean the infimum of the set $$ \{ f(k,l) \mid (k,l)\in K\times L \}$$ which is hopefully a subset of $\mathbb R$ or some other ordered set where you can speak of infima.

You'll need to deduce from the context what the index sets $K$ and $L$ are.

Note that if there are infinitely many possible $k$s or $l$s, the set above can be infinite, and in that case "infimum" may not be the same as "minimum"