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)
“To die proudly when it is no longer possible to live proudly. Death freely chosen, death at the right time, brightly and cheerfully accomplished amid children and witnesses: then a real farewell is still possible, as the one who is taking leave is still there; also a real estimate of what one has wished, drawing the sum of one’s life—all in opposition to the wretched and revolting comedy that Christianity has made of the hour of death.”
—Friedrich Nietzsche (1844–1900)