The EnKU is the unique exact affine conditioning map for all but a small symmetric class inside the set E^EnKU, which is essentially the largest possible set admitting such maps.
Rajba , On multiple decomposability of probability measures on r , Demonstratio Mathematica, 34 (2001), pp
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Exact affine conditioning beyond Gaussians: a unique characterization of the ensemble Kalman update
The EnKU is the unique exact affine conditioning map for all but a small symmetric class inside the set E^EnKU, which is essentially the largest possible set admitting such maps.