Cylinder Set Measures Versus True Measures
A cylinder set measure on E is not actually a measure on E: it is a collection of measures defined on all finite-dimensional images of E. If E has a probability measure μ already defined on it, then μ gives rise to a cylinder set measure on E using the push forward: set μT = T∗(μ) on FT.
When there is a measure μ on E such that μT = T∗(μ) in this way, it is customary to abuse notation slightly and say that the cylinder set measure "is" the measure μ.
Read more about this topic: Cylinder Set Measure
Famous quotes containing the words cylinder, set, measures and/or true:
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—Henry Brooks Adams (1838–1918)
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—Alfred Döblin (1878–1957)
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—Henry David Thoreau (1817–1862)
“The true mirror of our discourse is the course of our lives.”
—Michel de Montaigne (1533–1592)