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Yes, it is, in a way. And seeing is measuring, too, I suppose. But both "measure" rather crudely with a high baseline threshold. An electron microscope can "measure" better than the human eye. Lab gear can "measure" better than the human ear. Bottom line: you can't hear things that can't be measured, but you can measure things that can't be heard.
Hearing is measuring, in one sense. But, sound
perception is not the direct outcome of this 'ear measurement'. Your brain makes hard work trying to make some sense out of this measurement data. Your brain has spend years on learning to interpret this data, and whenever you listen to something the brain tries to make the most logical decision based on the data it has available (hearing, seeing, feeling, knowing, expecting,...). If you reduce these 'info channels', which actually happens with headphone listening, then it's quite easy to fool your brain to hear things that doesn't exist.
Good example is that if you are a regular hat user and you put on your hat while listening to something the sound doesn't change, because your brain has learned to adapt to this change. With a microphone you can easily measure this.
Another, different, example is that if you have a series of harmonic pitches, e.g., 200Hz, 300Hz, 400Hz,..., with appropriate gains, you can hear the (non-existent) 100Hz frequency. This is called a 'missing fundamental' -phenomenon. If you know what kind of data ear outputs, and brain being used to that many sounds have a periodic series of pitch components, this is actually quite logical interpretation of the data.
So, the bottom line is that
you can hear things that can't be measured, and you can also measure things that can't be heard.