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Definition: For any E in X, where X is any set, define M(E) = infinity if E is an infinite set, and let M(E) be then number of points in E if E is finite. M is called the counting measure on X.

Let f(x) : R -> [0,infinity)
f(j) = { a_j , if j in Z, a if j in RZ}
( Z here is counting numbers, R is set of real numbers)

Let M be the counting measure. Find integral over R of f dM.

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This is a counting measure/integral problem.

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Counting measure problem (integrals)

Definition: For any E in X, where X is any set, define M(E) = infinity if E is an infinite set, and let M(E) be then umber of points in E if E is finite. M is called the counting measure on X.

Let f(x) : R -> [0,infinity)
f(j) = { a_j , if j in Z, a if j in RZ}
( Z here is counting numbers, R is set of real numbers)

Let M be the counting measure. Find integral over R of f dM.
My ...

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