  The mass of the Higgs boson is measured in the $H \rightarrow ZZ^*
\rightarrow 4\ell$ decay channel. The analysis uses proton-proton collision
data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV
recorded by the ATLAS detector between 2015 and 2018, corresponding to an
integrated luminosity of 139 fb$^{-1}$. The measured value of the Higgs boson
mass is $124.99\pm0.18\text{(stat.)}\pm0.04\text{(syst.)}$ GeV and is based on
improved momentum-scale calibration for muons relative to previous
publications. The measurement also employs an analytic model that takes into
account the invariant-mass resolution of the four-lepton system on a per-event
basis and the output of a deep neural network discriminating signal from
background events. This measurement is combined with the corresponding
measurement using 7 and 8 TeV $pp$ collision data, resulting in a Higgs boson
mass measurement of $124.94\pm0.17\text{(stat.)}\pm0.03\text{(syst.)}$ GeV.
