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The natural "Lebesgue measure" on S 1 is then the push-forward measure f ∗ (λ). The measure f ∗ (λ) might also be called "arc length measure" or "angle measure", since the f ∗ (λ)-measure of an arc in S 1 is precisely its arc length (or, equivalently, the angle that it subtends at the centre of the circle.)
In finance, a T-forward measure is a pricing measure absolutely continuous with respect to a risk-neutral measure, but rather than using the money market as numeraire, it uses a bond with maturity T. The use of the forward measure was pioneered by Farshid Jamshidian (1987), and later used as a means of calculating the price of options on bonds .
X is a Brownian motion with respect to P, i.e., the law of X with respect to P is the same as the law of an n-dimensional Brownian motion, i.e., the push-forward measure X ∗ (P) is classical Wiener measure on C 0 ([0, ∞); R n). both X is a martingale with respect to P (and its own natural filtration); and
For example, if the map φ is not surjective, there is no natural way to define such a pushforward outside of the image of φ. Also, if φ is not injective there may be more than one choice of pushforward at a given point. Nevertheless, one can make this difficulty precise, using the notion of a vector field along a map.
Pushforward measure, measure induced on the target measure space by a measurable function; Pushout (category theory), the categorical dual of pullback; Direct image sheaf, the pushforward of a sheaf by a map; Fiberwise integral, the direct image of a differential form or cohomology by a smooth map, defined by "integration on the fibres"
Dextrorotation and laevorotation (also spelled levorotation) [1] [2] in chemistry and physics are the optical rotation of plane-polarized light.From the point of view of the observer, dextrorotation refers to clockwise or right-handed rotation, and laevorotation refers to counterclockwise or left-handed rotation.
A Borel measure on a separable Banach space is said to be a non-degenerate (centered) Gaussian measure if, for every linear functional except =, the push-forward measure is a non-degenerate (centered) Gaussian measure on in the sense defined above.
In fact, if either measure is absolutely continuous with respect to the Haar measure, then so is their convolution. [34] If μ and ν are probability measures on the topological group (R,+), then the convolution μ∗ν is the probability distribution of the sum X + Y of two independent random variables X and Y whose respective distributions ...