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:
“One measure of a civilization, either of an age or of a single individual, is what that age or person really wishes to do. A man’s hope measures his civilization. The attainability of the hope measures, or may measure, the civilization of his nation and time.”
—Ezra Pound (1885–1972)
“There is in him, hidden deep-down, a great instinctive artist, and hence the makings of an aristocrat. In his muddled way, held back by the manacles of his race and time, and his steps made uncertain by a guiding theory which too often eludes his own comprehension, he yet manages to produce works of unquestionable beauty and authority, and to interpret life in a manner that is poignant and illuminating.”
—H.L. (Henry Lewis)
“Whenever the weather licks the pilot instead of him lickin’ the weather, he’s finished. The first time makes the second time easier. And the first thing he knows, he’s in trouble when the weather is perfect.”
—Frank W. Wead (1895?–1947)
“Love once
Tipped the scales but now is shadowed, invisible,
Though mysteriously present, around somewhere.”
—John Ashbery (b. 1927)