Let $C_\lambda$ be the classical Cantor set associated to a real number $0<\lambda<\frac{1}{2}$, as defined for example in the book of K. J. Falconer The geometry of fractal sets. I recall briefly the construction. Starting with the unit interval, we remote from the center of the interval an interval of length $1-2\lambda$. After $n$ steps, we obtain $2^n$ intervals equally spaced out, each one of length $\lambda^n$. For the Hausdorff measure $\mathscr{H}^s$ of dimension $s$, we use the function $g(S)=\text{diam}(S)^s$ for the Caratheordory construction and we define the upper density of a set $A\subset \mathbb{R}^n$, at a point $x\in\mathbb{R}^n$ by $$ \Theta^{*s}(A,x)=\limsup_{r\rightarrow 0}\frac{\mathscr{H}^s(A\cap B(x,r))}{(2r)^s} $$ and for the lower density $\Theta_*^s$ we replace $\limsup$ by $\liminf$. We can prove that $\dim C_\lambda=\frac{\log 2}{\log(1/\lambda)}=s_\lambda$, and even $\mathscr{H}^{s_\lambda}(C_\lambda)=1$, and I wanted to obtain precise estimates for the upper and lower density of $C_\lambda$. In fact I think that I managed to prove that for all $x\in C_\lambda$, we have $$ 2^{-(s_\lambda+1)}\leq \Theta_*^{s_\lambda}(C_\lambda,x)\leq 2^{-s_\lambda}\leq \Theta^{*s_\lambda}(C_\lambda,x)\leq 1. $$ The problem is that I know that there is a lower bound more precise for $\Theta^{*s_\lambda}(C_\lambda,x)$, namely, a constant $c>2^{-s_\lambda}$, such that $\Theta^{*s_\lambda}(C_\lambda,x)\geq c$ for all $x\in C_\lambda$. I would like to get a confirmation of the validity of the calculated estimates, and I would really appreciate a hint for the last lower bound.