The final results of the search for the lepton flavour violating decay $$\mathrm {\mu }^+ \rightarrow \mathrm {e}^+ \mathrm {\gamma }$$ based on the full dataset collected by the MEG experiment at the Paul Scherrer Institut in the period 2009–2013 and totalling $$7.5\times 10^{14}$$ stopped muons on...