What are units-of-measure? e.g., what's a "kilometer"?

Hi Folks,

Consider this statement:

  "The length of the Yangtze River is 6300 kilometers."

What is a "kilometer"?

1. Is kilometer a class?  Is 6300 an instance of the kilometer class?
     kilometer class: {..., 6300, ...}

2. Is kilometer a function? e.g., kilometer(Yangtze) --> 6300
   In general: kilometer(physical object) --> number
   "The kilometer function maps a physical object to a number."

3. Is kilometer a property? e.g., a property of the Yangtze River 
   is kilometer (this doesn't quite sound right; perhaps there's
   another way of expressing this that is more natural?)

4. Is kilometer a label?  If so, then what's a label?

Or is it something else?  /Roger