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:
“I candidly confess that I have ever looked on Cuba as the most interesting addition which could ever be made to our system of States. The control which, with Florida, this island would give us over the Gulf of Mexico, and the countries and isthmus bordering on it, as well as all those whose waters flow into it, would fill up the measure of our political well-being.”
—Thomas Jefferson (1743–1826)
“Hygiene is the corruption of medicine by morality. It is impossible to find a hygienest who does not debase his theory of the healthful with a theory of the virtuous.... The true aim of medicine is not to make men virtuous; it is to safeguard and rescue them from the consequences of their vices.”
—H.L. (Henry Lewis)
“It is not time or opportunity that is to determine intimacy;Mit is disposition alone. Seven years would be insufficient to make some people acquainted with each other, and seven days are more than enough for others.”
—Jane Austen (1775–1817)
“In what camera do you taste
Poison, in what darkness set
Glittering scales and point
The tipping tongue?”
—Wallace Stevens (1879–1955)