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:
“Desire is creation, is the magical element in that process. If there were an instrument by which to measure desire, one could foretell achievement.”
—Willa Cather (1873–1947)
“Osteopath—One who argues that all human ills are caused by the pressure of hard bone upon soft tissue. The proof of his theory is to be found in the heads of those who believe it.”
—H.L. (Henry Lewis)
“Pluck down my officers, break my decrees,
For now a time is come to mock at form.”
—William Shakespeare (1564–1616)
“Love once
Tipped the scales but now is shadowed, invisible,
Though mysteriously present, around somewhere.”
—John Ashbery (b. 1927)