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:
“Physics investigates the essential nature of the world, and biology describes a local bump. Psychology, human psychology, describes a bump on the bump.”
—Willard Van Orman Quine (b. 1908)
“The history of literature—take the net result of Tiraboshi, Warton, or Schlegel,—is a sum of a very few ideas, and of very few original tales,—all the rest being variation of these.”
—Ralph Waldo Emerson (1803–1882)