For a sequence u_j:Ω⊂ Rⁿ→ R^m generating the Young measure ν_x, x∈Ω, Ball's Theorem asserts that a tightness condition preventing mass in the target from escaping to infinity implies that ν_x is a probability measure and that f(u_k)⇀<ν_x,f> in L¹ provided the sequence is equiintegrable. Here we show that Ball's tightness condition is necessary for the conclusions to hold and that in fact all three, the tightness condition, the assertion ∥ν_x∥=1, and the convergence conclusion, are equivalent. We give some simple applications of this observation.