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:
“Speech is the twin of my vision, it is unequal to measure itself,
It provokes me forever, it says sarcastically,
Walt you contain enough, why don’t you let it out then?”
—Walt Whitman (1819–1892)
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes “So much the worse for the facts: let them be altered,” instead of “So much the worse for my theory.””
—George Bernard Shaw (1856–1950)
“Now it is time to call attention
to our bed, a forest of skin
where seeds burst like bullets.
We are in our room. We are in
a shoe box. We are in a blood box.”
—Anne Sexton (1928–1974)
“Love once
Tipped the scales but now is shadowed, invisible,
Though mysteriously present, around somewhere.”
—John Ashbery (b. 1927)