Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Analysis Lebesgue Measure & Integral
Let 𝒩 ⊆ ℝ be a non-measurable set with respect to the Lebesgue measure on ℝ.
Consider the following statements:
𝑃: If 𝑀 = { 𝑥 ∈ 𝒩 ∶ 𝑥 is irrational }, then 𝑀 is Lebesgue measurable.
𝑄: The boundary of 𝒩 has positive Lebesgue outer measure.
Then
1
both 𝑃 and 𝑄 are TRUE
2
𝑃 is FALSE and 𝑄 is TRUE
3
𝑃 is TRUE and 𝑄 is FALSE
4
both 𝑃 and 𝑄 are FALSE
5
Question Not Attempted