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:
“By recognizing a favorable opinion of yourself, and taking pleasure in it, you in a measure give yourself and your peace of mind into the keeping of another, of whose attitude you can never be certain. You have a new source of doubt and apprehension.”
—Charles Horton Cooley (1864–1929)
“[Anarchism] is the philosophy of the sovereignty of the individual. It is the theory of social harmony. It is the great, surging, living truth that is reconstructing the world, and that will usher in the Dawn.”
—Emma Goldman (1869–1940)
“I’ve been cursed for delving into the mysteries of life. Perhaps death is sacred, and I’ve profaned it. Oh, what a wonderful vision it was. I dreamed of being the first to give to the world the secret that God is so jealous of, the formula for life. Think of the power, to create a man. And I did, I did it, I created a man. And who knows, in time I could have trained him to do my will. I could have bred a race, I might even have found the secret of eternal life.”
—William Hurlbut (1883–?)
“Love once
Tipped the scales but now is shadowed, invisible,
Though mysteriously present, around somewhere.”
—John Ashbery (b. 1927)