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.
Read more about this topic: Minkowski Addition
Famous quotes containing the words essential and/or sum:
“I am not so foolish as to declaim against forms. Forms are as essential as bodies; but to exalt particular forms, to adhere to one form a moment after it is outgrown, is unreasonable, and it is alien to the spirit of Christ.”
—Ralph Waldo Emerson (1803–1882)
“the possibility of rule as the sum of rulelessness:”
—Archie Randolph Ammons (b. 1926)