Additive Function - Search Videos

The additive inverse is a specific number, and every real number has one! That is, these inverses occur in pairs. We'll look at what their properties are, how to find them, and the most common applications.

172K viewsOct 31, 2015

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For a measurable additive function f:R→R consider the functions... | Filo

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What Is Additive Manufacturing? | Built In

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Additive Identity | Definition, Properties & Example

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What Is Additive Manufacturing?

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Study.comElizabeth Friedl

$Strong law for additive functionals. Suppose p is irreducible and has stationary distribution π. Let f be a function that has ∑|f(y)| π(y)<∞. Let Tx^k be the time of the k th return to x. (i) Show that Vk^f=f(X(Tx^k)) ⋯ f(X(Tx^k 1-1)), k ≥1 are i.i.d. with E|Vk^f|<∞. (ii) Let Kn=inf{k: Tx^k ≥n} and show that (1)/(n) ∑m=1^Kn Vm^f →(E V1^f)/(Ex Tx^1)=∑f(y) π(y) Pμ- a.s (iii) Show that max1 ≤m ≤n Vm^|f| / n →0 and conclude (1)/(n) ∑m=1^n f(Xm) →∑y f(y) π(y) Pμ- a.s. for any initial distri$