Let $n\geq 2$, $A = \{x\in [0,1]^n|\exists t\in[0,1]: x = t\cdot (1,...,1)\}$, $B$ a Borel-measureable set and $f:\mathbb{R}^n\to\mathbb{R}$ a measureable function.
I can not make sense of the following expression, i.e., rewrite it in another form or interpret it in any sense.
$$\int_B f(x) d\delta_A(x)$$
I thought about rewriting it as a curve integral since $A$ is a curve in $[0,1]^n$ but I am not sure how.