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:

    Everything is good in due measure and strong sensations know not measure.
    Anton Pavlovich Chekhov (1860–1904)

    Lucretius
    Sings his great theory of natural origins and of wise conduct; Plato
    smiling carves dreams, bright cells
    Of incorruptible wax to hive the Greek honey.
    Robinson Jeffers (1887–1962)

    “What can be shown?
    What true love be?
    All could be known or shown
    If Time were but gone.”
    William Butler Yeats (1865–1939)

    For these have governed in our lives,
    And see how men have warred.
    The Cross, the Crown, the Scales may all
    As well have been the Sword.
    Robert Frost (1874–1963)