In a data warehouse, should a measure be based on a fact or a dimension?

Let’s say there is a data warehouse created from a shop data. A fact is a single purchase of a product. There is a dimension that describes a customer.

There is a need to create a measure that stores a number of distinct customers. Can this measure be created based on customer identifier in the dimension table, or it needs to be fact table? In which cases one or the other solution is better?

Below I post a visualization based on an AdventureWorks2016 database:

Data warehouse example visualization based on a AdventureWorks2016 database.