Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Lebesgue Measure & Integral
Let f : [0, 1] → ℝ be a function. Which one of the following is a sufficient condition for f to be Lebesgue measurable?
1
|f| is a Lebesgue measurable function
2
There exist continuous functions g, h : [0, 1] → ℝ such that g ≤ f ≤ h on [0, 1]
3
f is continuous almost everywhere on [0, 1]
4
For each c ∈ ℝ, the set {x ∈ [0, 1] : f(x) = c} is Lebesgue measurable