Final answer:
To show that if a set T with m*(T)=2023, then there is a bounded subset S of T such that m*(S)>0.
Step-by-step explanation:
We want to show that if a set T with m*(T)=2023, then there is a bounded subset S of T such that m*(S)>0.
In measure theory, the outer measure m*(T) of a set T is defined as the infimum of the sum of lengths of countable sequences of intervals that cover T. If m*(T)=2023, it means that there exists such a sequence of intervals whose sum of lengths is equal to 2023.
We can take any one of these intervals, and define S as the bounded subset that contains only that interval. Since the interval has a positive length, the measure of S will be greater than zero.