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:
“What we know partakes in no small measure of the nature of what has so happily been called the unutterable or ineffable, so that any attempt to utter or eff it is doomed to fail, doomed, doomed to fail.”
—Samuel Beckett (1906–1989)
“The theory of truth is a series of truisms.”
—J.L. (John Langshaw)
“The principle of asceticism never was, nor ever can be, consistently pursued by any living creature. Let but one tenth part of the inhabitants of the earth pursue it consistently, and in a day’s time they will have turned it into a Hell.”
—Jeremy Bentham (1748–1832)
“Love once
Tipped the scales but now is shadowed, invisible,
Though mysteriously present, around somewhere.”
—John Ashbery (b. 1927)