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 measure of your quality as a public person, as a citizen, is the gap between what you do and what you say.”
—Ramsey Clark (b. 1927)
“The human species, according to the best theory I can form of it, is composed of two distinct races, the men who borrow and the men who lend.”
—Charles Lamb (1775–1834)
“Every time a woman makes herself laugh at her husband’s often-told jokes she betrays him. The man who looks at his woman and says “What would I do without you?” is already destroyed.”
—Germaine Greer (b. 1939)
“It cannot but affect our philosophy favorably to be reminded of these shoals of migratory fishes, of salmon, shad, alewives, marsh-bankers, and others, which penetrate up the innumerable rivers of our coast in the spring, even to the interior lakes, their scales gleaming in the sun; and again, of the fry which in still greater numbers wend their way downward to the sea.”
—Henry David Thoreau (1817–1862)