  The discovery of the Higgs particle at 125 GeV is demanding a detailed
knowledge of the properties of this fundamental component of the Standard
Model. To that aim various proposals of electron and muon colliders have been
put forward for precision studies of the partial widths of the various decay
channels. It is shown that in the case of a Higgs factory through a muon
collider, sizeable radiative effects - of order of 50% - must be carefully
taken into account for a precise measurement of the leptonic and total widths
of the Higgs particle. Similar effects do not apply in the case of Higgs
production in electron-positron colliders.
