What is an example of an unbounded, open set with a finite outer measure? The outer measure is defined as $$m^*(A) = \left\{\sum_{n=1}^\infty \ell(I_n) : I_n \ \text{is an open interval and} \ A \subseteq \bigcup_{n=1}^\infty I_n\right\}$$
Example of an outer measrue
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real-analysis
measure-theory
1 Answers
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Try $(0,\frac 1 2 ) \cup (1,1+\frac 1 {2^2}) \cup (2,2+ \frac 1 {2^3}) \cup (3,3 + \frac 1 {2^4}) \cup \dots$.