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:
“Might was the measure of right.”
—Marcus Annaeus Lucan (39–65)
“Many people have an oversimplified picture of bonding that could be called the “epoxy” theory of relationships...if you don’t get properly “glued” to your babies at exactly the right time, which only occurs very soon after birth, then you will have missed your chance.”
—Pamela Patrick Novotny (20th century)
“Superstition saw
Something it had never seen before:
Brown eyes that loved without a trace of fear,
Beauty so sudden for that time of year.”
—Jean Toomer (1894–1967)
“Love once
Tipped the scales but now is shadowed, invisible,
Though mysteriously present, around somewhere.”
—John Ashbery (b. 1927)