Juxtaposition Measure and the Resolution of Classical Non-Measurable Sets

We introduce juxtaposition addition (): identical elements placed side by side yield 00⋯=1, corresponding to 0×∞=1 (1D) and 0ₛ×∞ₛ=1ₛ (s-dimensional). Under this regime, Carath\'eodory's condition holds identically for all sets---no non-measurable sets exist. Seven classical non-measurable constructions (Vitali, Bernstein, Sierpi\'nski, Hamel, Ulam, Banach--Tarski, Hausdorff) are resolved with unique phase-proportion assignments determined by construction rules. The Cantor set has 1D juxtaposition measure $2/3$ and s-dimensional measure 1ₛ, aligning with Hausdorff normalization. Arithmetic operations and the four-step calculus procedure are unified as expansion/contraction duality repeated across the two regimes. Classical measure theory is not overthrown but completed at the microscopic level.