Suppose $G$ is a topological group with probability measure $\mu$. Define $\lambda=\sum_{n=0}\frac{1}{2^{n+1}}\mu^{n}$, where $\mu^0$ is Dirac measure at identity and $\mu^n$ is the convolution of measure $\mu$ $n$ times w.r.t $\mu$.
How does one show that $\textrm{supp}(\lambda)=T_{\mu}\cup\{1\}$, where $T_{\mu}$ is the smallest closed semigroup containing the support of $\mu$?