Is the following use of indices correct?

Question

Is the following use of indices correct? A vector $\langle x_i, x_{i+1},...,x_{i+k}\rangle$ is given. For every such vector a function is defined through $$\mu=\frac{\sum_{j=0}^k I_A(x_{i+j})}{k+1}\,,$$ where $I_A$ is the indicator function of some set A. Is it mathematically correct notation? In particular the use of $i+j$ as sub index.

Answer 1

As mentioned in the comments above, the notation is correct.