This implies that "'the product of two functions of bounded variation is again a function of bounded variation "', therefore "'
12.
This implies that "'the product of two functions of bounded variation is again a function of bounded variation "', therefore "'
13.
Basically they introduced two new kind of functions of bounded variation, as the various sections found in a lot of important monographs in mathematics and mathematical physics testify.
14.
If " g " is not of bounded variation, then there will be continuous functions which cannot be integrated with respect to " g ".
15.
Another characterization states that the functions of bounded variation on a compact interval are exactly those which can be written as a difference, where both and are bounded monotone.
16.
Doing the same, but using the Riemann Stieltjes integral, along with an appropriate function of bounded variation, gives a definition of integral equivalent to the Lebesgue Stieltjes integral.
17.
Also, PCA is a traditional way of fitting a closed ellipsoid to a Gaussian cloud of points ( whatever their dimension ) : this suggests the concept of bounded variation.
18.
One can prove that if \ mu is a vector measure of bounded variation, then \ mu is countably additive if and only if | \ mu | is countably additive.
19.
In the case of several variables, a function defined on an open subset of ! " n " is said to have bounded variation if its vector-valued finite Radon measure.
20.
In the second, he contrasts the deductivist and heuristic approaches and provides heuristic analysis of some'proof generated'concepts, including uniform convergence, bounded variation, and the Carath�odory definition of a measurable set.
