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The way your data is structured, I am not aware of any way to get around calculating whether each measure is null or not null.
IF NOT(ISNULL([M1])) THEN 1 ELSE 0 END
IF NOT(ISNULL([M2])) THEN 1 ELSE 0 END
IF NOT(ISNULL([M15])) THEN 1 ELSE 0 END
Then you should be able to make your percent as SUM([NonNull Measures]) / SUM(Number of Records) as a calculated field to include on the view.
If you changed the structure of your data so that each unique dimension combination AND measure had its own row, (I call this "unpivoted data") then I believe you could get to it without having to create a field for each separate measure.
You'd simply create a single calculated field of IF NOT(ISNULL([M1])) THEN 1 ELSE 0 END and put your [Measure] on the columns shelf to split the view.
ID Area Measure Value 1 A M1 9 1 A M2 2 1 A M3 3 1 A M4 0 1 A M5 9 2 B M1 9 2 B M2 2 2 B M3 3 2 B M4 0 2 B M5 [null]