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)
“... liberal intellectuals ... tend to have a classical theory of politics, in which the state has a monopoly of power; hoping that those in positions of authority may prove to be enlightened men, wielding power justly, they are natural, if cautious, allies of the “establishment.””
—Susan Sontag (b. 1933)
“Men have died from time to time, and worms have eaten them, but not for love.”
—William Shakespeare (1564–1616)
“In what camera do you taste
Poison, in what darkness set
Glittering scales and point
The tipping tongue?”
—Wallace Stevens (1879–1955)