What conditions are necessary to prove that the upper and lower integrals of a bounded function exist?
1
a, b ∈ \(\mathbb R\), a > b, and f: [a, b] → \(\mathbb R\)
2
a, b ∈ \(\mathbb R\), a < b, and f: [a, b] → \(\mathbb R\) be bounded
3
a, b ∈ \(\mathbb R\), a < b, and f:[a, b] → \(\mathbb Z\) be bounded
4
a, b ∈ \(\mathbb Z\), a < b, and f:[a, b] → \(\mathbb R\) be bounded