Unfortunately, I cannot access the link provided. However, in general, finding the Lebesgue outer measure of a set involves constructing a sequence of sets that covers the set of interest and whose measures can be easily calculated. The Lebesgue outer measure is then defined as the infimum of the sum of the measures of these covering sets.
For example, if the set of interest is a subset of the real line, we can construct a sequence of open intervals that covers the set, and whose lengths add up to no more than a predetermined number (e.g. the diameter of the set). The Lebesgue outer measure is then defined as the infimum of the sums of the lengths of these covering intervals.
If the set of interest is more complicated, we may need to use different covering sets, such as rectangles in 2D or balls in higher dimensions. The key is to construct the sequences of covering sets carefully so that they converge to the set of interest while their measures are kept under control.
How do we find the Lebsgue outer measure of below set
Set : drive[DOT]google(fot)com/file/d/1-ZwjDEF8LO5nLPEMHPgx8oNArUDQi19b/view?usp=drivesdk
I know that both of them have Lebesgue outer measure of O, but not sure how to take the lebesgue outer measure of the whole set.
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