Well, You can try putting Measure Values field under Measures shelf into Filter Shelf!
THat should work!
Hope it helps!
I would recommend using a parameter rather than trying to use "Measure Names" as a quick filter--you cannot edit the filter selections and there are other limitations of using Measure Names. The link above should provide a good starting point.
Using a parameter, you can let users choose whatever measures they want to display and you'll have a bit more flexibility.