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:
“Poetry is emotion put into measure. The emotion must come by nature, but the measure can be acquired by art.”
—Thomas Hardy (18401928)
“Thus the theory of description matters most.
It is the theory of the word for those
For whom the word is the making of the world,
The buzzing world and lisping firmament.”
—Wallace Stevens (18791955)
“Vanity of science. Knowledge of physical science will not console me for ignorance of morality in time of affliction, but knowledge of morality will always console me for ignorance of physical science.”
—Blaise Pascal (16231662)
“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)