For almost every Hölder observable φ with respect to certain Wiener-like measures on C[0,1], the map λ to the integral against μ_λ is almost nowhere differentiable for small λ and almost everywhere differentiable for large λ.
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Linear Response for Bernoulli Convolutions
For almost every Hölder observable φ with respect to certain Wiener-like measures on C[0,1], the map λ to the integral against μ_λ is almost nowhere differentiable for small λ and almost everywhere differentiable for large λ.