Autocorrelation of heaviside functions
@JRE has a good point - a better match for DSP.  But in any case,

$$\int_{-T}^Tu(t+\tau)\cdot u(t)dt=\int_{-T}^{0}0dt+\int_{0}^T1dt=T$$
$$\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^Tu(t+\tau)\cdot u(t)dt=\lim_{T \to \infty}\frac{T}{2T}=\frac{1}{2}$$