Crossing a horizontal nonlinear resonance is the approach that can be used to split a beam
in several beamlets with the goal to perform multi-turn extraction from a circular particle
accelerator. Such an approach has been successfully implemented in the CERN Proton Synchrotron and
is used routinely for the production of high-intensity proton beams for fixed-target physics at
the Super Proton Synchrotron. Recently, thanks to the deployment of diamond detectors, originally
installed to monitor the beam losses at extraction, it has been possible to measure the horizontal
beam emittance of the split beam just prior to extraction. This is the first time that an
emittance measurement is attempted for split beams, i.e. in a regime of highly nonlinear beam
dynamics. In this paper, the technique is presented and its application to the analysis of the
experimental data is presented and discussed in detail. This result is essential for the
performance assessment of the splitting process and for the design of further performance
improvements.