This subject is treated by many, including myself, in a somewhat simplistic way... on the other side a full discussion would involve a lot of math so I have asked Jakob to try translating those concepts into english wording and in pills:
* If you measure in a single point you cannot know what is common, and what is different due to room reflections, in different points in the listening area.
Without that information it's impossible to tell what is robustly invertible.
Using information from multiple measurements the inverse can be made as detailed as allowed by the spatial variability.
* By applying heavy smoothing to a single point it is often possible to capture the behavior in neighboring points as well, as the smoothing will remove most of the details.
(Minphase) filters based on such a model are likely to be spatially robust in an area around the measured position.
The resolution of the ear have very little to do with the performance of this filter, what matters is if the filter is valid for the behavior to be corrected in points around the measured point.
* For this to be true the filter will have to be smooth in most cases, but with some exceptions.
Assume you have a speaker with a jagged response placed in a room that does not affect the response significantly.
In this case the response will be similar in a large area, and it is possible to design a filter based on a single measurement that is spatially robust and has a high resolution.
But using a single measurement it is not possible to know what resolution can be used as there is no information on what is common and what is different.
In cases where the direct wave is not dominant averaging over space corresponds reasonably well with averaging over frequency.
* If you want to correct the impulse response (not just the amplitude response) and make sure the resulting filter do not introduce pre-ringings you again need information from more than one point.
It is imperative to find out what is varying and what is static, and that information cannot be synthesized from a single measurement.
Again, various smoothing techniques (in the time domain this time) can be used to make do with only a single measurements, and sometimes the smoothed model will be a good approximation of the behavior close to the measured point; sometimes it won't be.
How well a measurement can be made to represent a large area varies from room to room and speaker to speaker.
This is it, ciao
Flavio