Using a data set of 2.93 fb$^{-1}$ taken at a center-of-mass energy of $sqrt{s}$ = 3.773 GeV with the BESIII detector at the BEPCII collider, we measure the process $e^+e^-rightarrow J/psigammarightarrow mu^+mu^-gamma$ and determine the product of the branching fraction and the electronic width $mathcal B_{mumu}cdot Gamma_{ee} = (333.4 pm 2.5_{rm stat} pm 4.4_{rm sys})$~eV. Using the earlier-published BESIII result for $mathcal B_{mumu}$ = (5.973 $pm$ 0.007$_{rm stat}$ $pm$ 0.037$_{rm sys}$)%, we derive the $J/psi$ electronic width $Gamma_{ee}$~= (5.58 $pm$ 0.05$_{rm stat}$ $pm$ 0.08$_{rm sys}$) keV.
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