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 love the pride whose measure is its own eminence and not the insignificance of someone else.”
—Franz Grillparzer (1791–1872)
“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)
“A “modern” man has nothing to add to modernism, if only because he has nothing to oppose it with. The well-adapted drop off the dead limb of time like lice.”
—Elias Canetti (b. 1905)
“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)