Is this notation for an inner product common?

Question

In my measure theory and integration course we learned about line integrals and surface integrals. My lecturer uses the notation $(u | v)_{\mathbb{R}^n}$ to denote the (Euclidean) dot product of two vectors $u, v\in \mathbb{R}^n$, which is a notation that I have never seen before except for the books of Daniel Stroock on integration (books that my lecturer mentioned and recommended to us-otherwise I would have never heard of these books since I don't think they are that popular, but I may be wrong since I am a novice when it comes to measure, integration and related aspects). This means that if we, say, integrate some function $F$ on some space curve $\sigma$, then the notation used would be $$\int_{\sigma} (F|dl)_{\mathbb{R}^3}$$ due tot the way we denote the dot product.
Needless to say that in any online resource (and any books I have) this is not the way to denote things.
So, is this notation popular or is it some weird one used by only a handful of people? My hunch is that it is common in certain areas of mathematics (I suspect PDEs/functional analysis because this is my lecturer's research field, but I haven't taken any course on either of those subjects, so I really can't say if my hunch is correct) and certainly not at the basic level (i.e. a regular multivariable calculus class let's say), this being the reason that it seemed weird to me.