[kskz]

Lebesgue measure is actually simpler than Borel measure, since it includes all null sets for convenience.

Yes, you could not talk about Lebesgue measure at all. However, the importance of theory is that you gain a deeper understanding of the abstract objects that the code is supposed to represent in the first place. This in turn, can have practical applications.

For example, you could implement a Fibonacci function using recursion as usual. But if you study the math a bit more deeply, then you can discover Binet's formula and get it in constant time.