A hearing aid comprising • an ear part (BTE; ITE) adapted for being mounted fully or partially at an ear or in an ear canal of a user, the ear part comprising ∘ a housing, ∘ at least one electrode (E1, E2,..., E N) located at a surface of said housing to allow said electrodes to contact the skin of a user when said ear part is operationally mounted on the user, the at least one electrode being adapted to pick up a low voltage electric signal from the user's brain, • an amplifier unit operationally connected to said electrode(s) and adapted for amplifying said low voltage electric signal(s) to provide amplified brain signal(s) (AEI; DAEI), • an input transducer for providing an electric audio input signal, • a signal processing unit, • an output transducer for converting an electric output signal to an acoustic output sound, • said signal processing unit being operationally connected ∘ to said amplifier unit and adapted to process said amplified brain signal(s) (AEI; DAEI) to provide a processed brain signal, ∘ to said input transducer and adapted to apply a time and frequency dependent gain to said electric audio input signal or a signal originating therefrom and to provide a processed audio output signal, and ∘ to said output transducer allowing said processed audio output signal to be presented to the user as a processed acoustic signal, wherein the hearing aid further comprises a signal generator (AEP-SG; ABR-SG) for generating an electric test signal (ABR-S) specifically adapted to be used in an auditory evoked potential measurement, the signal generator being operationally connected to said output transducer allowing said electric test signal (ABR-S) to be converted to an auditory test stimulus for being presented to a user together with said processed acoustic signal during use of the hearing aid, and wherein the hearing aid is adapted to record the auditory evoked potential response during daily use for some time, e.g. a few days, and to provide said processed brain signals based on long term averaging of said auditory evoked potential responses recorded over days. • an ear part (BTE; ITE) adapted for being mounted fully or partially at an ear or in an ear canal of a user, the ear part comprising ∘ a housing, ∘ at least one electrode (E1, E2,..., E N) located at a surface of said housing to allow said electrodes to contact the skin of a user when said ear part is operationally mounted on the user, the at least one electrode being adapted to pick up a low voltage electric signal from the user's brain, ∘ a housing, ∘ at least one electrode (E1, E2,..., E N) located at a surface of said housing to allow said electrodes to contact the skin of a user when said ear part is operationally mounted on the user, the at least one electrode being adapted to pick up a low voltage electric signal from the user's brain, • an amplifier unit operationally connected to said electrode(s) and adapted for amplifying said low voltage electric signal(s) to provide amplified brain signal(s) (AEI; DAEI), • an input transducer for providing an electric audio input signal, • a signal processing unit, • an output transducer for converting an electric output signal to an acoustic output sound, • said signal processing unit being operationally connected ∘ to said amplifier unit and adapted to process said amplified brain signal(s) (AEI; DAEI) to provide a processed brain signal, ∘ to said input transducer and adapted to apply a time and frequency dependent gain to said electric audio input signal or a signal originating therefrom and to provide a processed audio output signal, and ∘ to said output transducer allowing said processed audio output signal to be presented to the user as a processed acoustic signal, ∘ to said amplifier unit and adapted to process said amplified brain signal(s) (AEI; DAEI) to provide a processed brain signal, ∘ to said input transducer and adapted to apply a time and frequency dependent gain to said electric audio input signal or a signal originating therefrom and to provide a processed audio output signal, and ∘ to said output transducer allowing said processed audio output signal to be presented to the user as a processed acoustic signal,