non-Lebesgue measure for the Doubling map

Question

Does there exists invariant non Lebesgue probability measures for the doubling map $T:[0,1)\rightarrow [0,1]$ defined by

$ T(x)=2x \,\text{mod}(1)? $

So a probability measure different from $\lambda([a,b))=b-a$, but still invariant under $T$.