It's a measure of the material produced by Peter, for one, refuting the truth (6)
I believe the answer is:
denier
'it's a measure' is the definition.
(I have seen 'fine measure' mean 'denier' so perhaps 'measure' could also mean 'denier')
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for denier that I've seen before include "One refusing to accept" , "Units of weight in silks, nylon and other yarns" , "Conspiracist probably" , "One who doesn't believe" , "One refuses to acknowledge" .)