Solution
= Solution
For a <Borel set> $A\subseteq[0,1]$, the two inverse branches of the <tent map> are $y\mapsto y/2$ and $y\mapsto1-y/2$. Apart from their immaterial common endpoint,
$$
T^{-1}A
=\frac A2\ \cup\ \left(1-\frac A2\right).
$$
Each branch scales <Lebesgue measure> by $1/2$, and their images lie in opposite half-intervals. Hence
$$
m(T^{-1}A)=\frac12m(A)+\frac12m(A)=m(A).
$$
Also $m([0,1])=1$, so $m$ is an invariant probability measure.