VITALI SET CONSTRUCTION
STEP 10 / 15
The Measure Paradox — Case 2
Suppose m(V) > 0
If m(V) = ε > 0, then the countable sum of identical positive values diverges.
FORMAL
m(⋃ V_q) = ∑ m(V_q) = ∑ ε = ∞
⚠ PARADOX
But the union fits inside [-1,2] with measure 3. Contradiction: ∞ ≤ 3.
Non-measurable sets · Axiom of Choice · rotates daily