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:
“REASON, is half of it, SENSE; and the measure of heaven itself is but the measure of our present appetites and concoctions.”
—Laurence Sterne (1713–1768)
“The theory seems to be that so long as a man is a failure he is one of God’s chillun, but that as soon as he has any luck he owes it to the Devil.”
—H.L. (Henry Lewis)
“What time she lifteth up herself on high, she scorneth the horse
and his rider.
Hast thou given the horse strength? hast thou clothed his neck with thunder?”
—Bible: Hebrew Job (l. XXXIX, 17–19)
“For these have governed in our lives,
And see how men have warred.
The Cross, the Crown, the Scales may all
As well have been the Sword.”
—Robert Frost (1874–1963)