Time-scale Calculus - Measure Theory On Time Scales

Measure Theory On Time Scales

Associated with every time scale is a natural measure defined via

where denotes Lebesgue measure and is the backward shift operator defined on . The delta integral turns out to be the usual Lebesgue–Stieltjes integral with respect to this measure

and the delta derivative turns out to be the Radon–Nikodym derivative with respect to this measure

Read more about this topic:  Time-scale Calculus

Famous quotes containing the words measure, theory, time and/or scales:

    I measure myself
    Against a tall tree.
    I find that I am much taller,
    For I reach right up to the sun,
    With my eye....
    Wallace Stevens (1879–1955)

    No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.
    Anna Quindlen (20th century)

    Parents have railed against shelters near schools, but no one has made any connection between the crazed consumerism of our kids and their elders’ cold unconcern toward others. Maybe the homeless are not the only ones who need to spend time in these places to thaw out.
    Anna Quindlen (b. 1952)

    In what camera do you taste
    Poison, in what darkness set
    Glittering scales and point
    The tipping tongue?
    Wallace Stevens (1879–1955)