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 have thought a sufficient measure of civilization is the influence of good women.”
—Ralph Waldo Emerson (18031882)
“Dont confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.”
—Martin H. Fischer (18791962)
“I cannot exaggerate the waste of the Presidents time and the consumption of his nervous vitality involved in listening to congressmens intercession as to local appointments. Why should the President have to have his time taken up in a discussion over ... who shall be the postmistress of Devils Lake, in North Dakota? How should he be able to know ... who is best fitted to fill such a place?”
—William Howard Taft (18571930)
“As deaths have accumulated I have begun to think of life and death as a set of balance scales. When one is young, the scale is heavily tipped toward the living. With the first death, the first consciousness of death, the counter scale begins to fall. Death by death, the scales shift weight until what was unthinkable becomes merely a matter of gravity and the fall into death becomes an easy step.”
—Alison Hawthorne Deming (b. 1946)