Outer measure ( for better understanding)

Let I be a nonempty interval of real numbers. We define length of I by L(I) where I is open and bounded interval and otherwise define its length to be the difference of its endpoints. For a set
A of real numbers, consider the countable collections of I k nonempty open, bounded
intervals that cover A, that is, collections for which A is contained each such collection,
consider the sum of the lengths of the intervals in the collection. Since the lengths are positive
numbers, each sum is uniquely defined independently of the order of the terms. We define
the outer measure of A, m*( A), to be the infimum of all such sums.

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What is outer measure?
Outer measure in Hindi
Let I be a nonempty interval of real numbers. We define its length, 1(I), to be oo if I is
unbounded and otherwise define its length to be the difference of its endpoints. For a set
A of real numbers, consider the countable collections {Ik}'1 of nonempty open, bounded
intervals that cover A, that is, collections for which A C U' 1 Ik. For each such collection,
consider the sum of the lengths of the intervals in the collection. Since the lengths are positive
numbers, each sum is uniquely defined independently of the order of the terms. We define
the outer measure3 of A, m* (A), to be the infimum of all such sums, that is
m*(A) = inf I(Ik)
1k=1
ACCUHIk .
It follows immediately from the definition of outer measure that m* (0) = 0. Moreover, since
any cover of a set B is also a cover of any subset of B, outer measure is monotone in the
sense that
ifACB, then m*(A) m*(B).

In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical condition

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