Intensive properties clarification - Chemical thermodynamics

I just started learning chemical thermodynamics and have come upon the definitions for extensive and intensive properties. I had a great deal of confusion over the exact meaning of intensive properties, but I believe I have come to a proper understanding of it after doing some extra reading. I will present my understanding below, and I just need to clarify that this is exactly what intensive properties are.
  
  

Intensive properties are defined differently for homogeneous and heterogeneous systems. For homogeneous systems, intensive properties are those properties that possess the same value at different points within the system and for the system as a whole. For heterogeneous systems, it no longer has anything to do with the value of the property for the system as a whole, but instead transforms into a local property, concerning only small volume elements within the system.  
  

Is this correct, or is there some brushing up needed? As of now I am only concerned with the most general understanding of intensive properties. Hope you could shed some light on this. Thank you.


