The "M" used to be used to represent molarity, the number of moles of a substance per liter of solution, so molarity per liter doesn't really make sense. The term is deprecated now but moles/liter is OK.
I'm sure it means a 4.5 millimolar solution, that is 4.5 mmol per liter of solution, but that should be written 4.5 mmol/L.
The small "m" was used for molality, 1 mole per kilogram of solvent, but obviously could be confused with meter.
Here's a link:
http://environmentalchemistry.com/yogi/ ... ality.html
