On the difference between consecutive zeros of the Riemann zeta function

Let 0 < γ₁ ≤ γ₂ ≤ … be the imaginary part of the zeros, $\text{λ =}\text{lim}{}_{\mathrm{n}}\text{(γ}{}_{\mathrm{n}}\text{? γ}{}_{\mathrm{n\; ?\; 1}}\text{)(}\text{log}\text{γ}{}_{\mathrm{n}}\text{2π}\text{)}$ and $\text{μ =}\text{lim}{}_{\mathrm{n}}\text{(γ}{}_{\mathrm{n}}\text{? γ}{}_{\mathrm{n\; ?\; 1}}\text{)(}\text{log}\text{γ}{}_{\mathrm{n}}\text{2π}\text{)}$. Assuming the Riemann hypothesis, it is known that μ ≤ 0.68 and λ > 1. One suspects that μ = 0 and λ = +∞. The object of this note is to show that λ ≥ 1.9.