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:
“Letters are above all useful as a means of expressing the ideal self; and no other method of communication is quite so good for this purpose.... In letters we can reform without practice, beg without humiliation, snip and shape embarrassing experiences to the measure of our own desires....”
—Elizabeth Hardwick (b. 1916)
“The theory of rights enables us to rise and overthrow obstacles, but not to found a strong and lasting accord between all the elements which compose the nation.”
—Giuseppe Mazzini (1805–1872)
“There comes a time in the affairs of men when they must prepare to defend not their homes alone but the tenets of faith and humanity on which their churches, their governments and their very foundations are set. The defense of religion, of democracy and of good faith among nations is all the same fight. To save one, we must now make up our minds to save all.”
—Franklin D. Roosevelt (1882–1945)
“Love once
Tipped the scales but now is shadowed, invisible,
Though mysteriously present, around somewhere.”
—John Ashbery (b. 1927)