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.


Read more about this topic:  Minkowski Addition

Famous quotes containing the words essential and/or sum:

    The essential function of art is moral.... But a passionate, implicit morality, not didactic. A morality which changes the blood, rather than the mind.
    —D.H. (David Herbert)

    No, the five hundred was the sum they named
    To pay the doctor’s bill and tide me over.
    It’s that or fight, and I don’t want to fight
    I just want to get settled in my life....
    Robert Frost (1874–1963)