We discuss some general aspects of 'multifractal scaling' in the conte
xt of continuum Lagrangian field theories and, in particular, an obser
vation of Duplantier and Ludwig that sequences of scaling variables wh
ich couple additively in their operator product expansion (OPE) exhibi
t multifractal scaling of their integer moments. We show that, for pos
itive variables, multifractal scaling of the integer moments implies,
along subsequences, multifractal scaling of all continuous moments and
, automatically, 'subadditivity' of the scaling exponent in the moment
index. A perturbative criterion of positivity is suggested. Finally,
some prospects for additively-coupled sequences and multifractal scali
ng in stable Lagrangian field theories are considered.