Short VersionIn the values tab in the properties, for your measure don't use the Auto aggregation method.
Change the Aggregation method to anything else (sum, avg....) and the BY option appears.
Now you can control the aggregation "by" feature of the measure.
Long VersionI had a data set with Customers income. Breaking the data by Regions I could see the difference of income between Regions:
I wanted to be sure that this is not because of significant variation of income between the Regions. I switched the Income to Avg. But nothing happened.
This is quite logical since the average is by Regions. I wanted to have an average for each Region by the income of every Customer in that Region. I can easily set the by parameter to Customer_Id and get the required result.