[mmmmpancakes]

> It means a small change in x.

So here is the issue. "A small change in x" is a concept that is relevant and meaningful for Riemann integration: it represents that the integral is defined as a limit of Riemann sums as the change in x becomes infinitely small.

But this is not relevant for Lebesgue integration! We are not taking a limit of Riemann sums and there is not a limit of change in x getting arbitrarily small. What matters is the measure (and the definition of the integral in terms of simple functions is something entirely different).

So you see using dx this way in the context of Lebesgue integration seems like a potential source of confusion, not simplification.

This is why i ask what dx means. Either it represents the standard Lebesgue measure on R (this is valid and a special case of the notation d\mu(x) since \mu is the identity function), or it is nonsense that potentially confuses concepts from other integration theories.

This is why mathematicians don't like your idea. They encounter many students who are confused about this distinction and don't find that it's a useful simplification.