Counting measure

Counting measure assigns to a set its cardinality, with value infinity for an infinite set.

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- Series as a Lebesgue integral against counting measure Counting measure

Series as a Lebesgue integral against counting measure

For

f : N \to [0, \infty]

,

\int_{N} f d # = \sum_{n = 1}^{\infty} f (n) := sup_{F \subseteq N finite} \sum_{n \in F} f (n) .

A complex-valued function is integrable for counting measure exactly when its series is absolutely convergent.

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Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 23H / c / Solution

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