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:
“Perpetual modernness is the measure of merit, in every work of art; since the author of it was not misled by anything short- lived or local, but abode by real and abiding traits.”
—Ralph Waldo Emerson (1803–1882)
“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)
“Muriel Bedford: It isn’t every day that your only son gets married.
Judge Bedford: He’s your son, too, Muriel. I mean it’s about time you started taking half the blame.”
—Dale Launer (b. 1953)
“In what camera do you taste
Poison, in what darkness set
Glittering scales and point
The tipping tongue?”
—Wallace Stevens (1879–1955)