Measurements and calculations of the air activation at a high-energy proton accelerator are described. The quantity of radionuclides released outdoors depends on operation scenarios including details of the air exchange inside the facility. To improve the prediction of the air activation levels, the MARS15 Monte Carlo code radionuclide production model was modified to be used for these studies. Measurements were done to benchmark the new model and verify its use in optimization studies for the new DUNE experiment at the Long Baseline Neutrino Facility (LBNF) at Fermilab. The measured production rates for the most important radionuclides - $^{11}$C, $^{13}$N, $^{15}$O and $^{41}$Ar - are in a good agreement with those calculated with the improved MARS15 code.