Since "amount of matter" is measured as an object's mass and "a given space" is measured as volume, the amount of matter in an a given space should equal mass/volume. Mass divided by volume is an object's density. Acceptable units of density include: grams/liters, kilograms/cubic meters, slugs/cubic inch, slugs/cubic foot, and many others.
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density
The amount of matter is given space is mass.
No, mass is not the amount of matter in a given space. It is actually density.
This is a very unspecific question, the amount of matter in a given space depends on what's in that space, and how much of it there is (as well as how dense it is).
density