It's a measure of the material produced by one of those dismissing 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 cannot 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 "Unit of weight for fine material, silk or nylon" , "Measurement of fineness in silk, nylon etc" , "Units of weight in silks, nylon and other yarns" , "old coin" , "Unit of weight of nylon, etc" .)