  We demonstrate an experimental method for measuring quantum state
degeneracies in bound state energy spectra. The technique is based on the
general principle of detailed balance, and the ability to perform precise and
efficient measurements of energy-dependent tunnelling-in and -out rates from a
reservoir. The method is realized using a GaAs/AlGaAs quantum dot allowing for
the detection of time-resolved single-electron tunnelling with a precision
enhanced by a feedback-control. It is thoroughly tested by tuning orbital and
spin-degeneracies with electric and magnetic fields. The technique also lends
itself for studying the connection between the ground state degeneracy and the
lifetime of the excited states.
