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:
“God is a concept by which we measure our pain.”
—John Lennon (1940–1980)
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)
“Every time a man unburdens his heart to a stranger he reaffirms the love that unites humanity.”
—Germaine Greer (b. 1939)
“Love once
Tipped the scales but now is shadowed, invisible,
Though mysteriously present, around somewhere.”
—John Ashbery (b. 1927)