Minkowski Addition - Essential Minkowski Sum

There is also a notion of the essential Minkowski sum +e of two subsets of Euclidean space. Note that the usual Minkowski sum can be written as

Thus, the essential Minkowski sum is defined by

where μ denotes the n-dimensional Lebesgue measure. The reason for the term "essential" is the following property of indicator functions: while

it can be seen that

where "ess sup" denotes the essential supremum.


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