[FredZarguna]

Consider the intervals: A = (-∞, 12] and B = (-∞, 32] both intervals are ∈ ℬ and thus Lebesgue measurable.

The characteristic function χ_A vanishes identically on (12, +∞) while the characteristic function χ_B has support only (-∞, 32]. Both functions are measurable, so their difference χ_B - χ_A is measurable.

Thus: ∫ χ_B - χ_A = ∫ χ_B - ∫ χ_A = 20.

Hope this helps more clearly illustrate the concepts of basic subtraction for small children.

[glock rocks]

Good Lord ...