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 thought of rhyme alone,
    For rhyme can beat a measure out of trouble
    And make the daylight sweet once more....
    William Butler Yeats (1865–1939)

    A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.
    Lionel Trilling (1905–1975)

    Once upon a time there were three little foxes
    Who didn’t wear stockings, and they didn’t wear sockses,
    But they all had handkerchiefs to blow their noses,
    And they kept their handkerchiefs in cardboard boxes.
    —A.A. (Alan Alexander)

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