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:
“The soul is no longer honored as it once was, but it still keeps appetite from being the measure of all things.”
—Mason Cooley (b. 1927)
“There never comes a point where a theory can be said to be true. The most that one can claim for any theory is that it has shared the successes of all its rivals and that it has passed at least one test which they have failed.”
—A.J. (Alfred Jules)
“For the time of towns is tolled from the world by funereal chimes, but in nature the universal hours are counted by succeeding tribes of animals and plants, and by growth of joy on joy.”
—Ralph Waldo Emerson (1803–1882)
“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)