Why Robert Bartle excluded the Riemann-Stieltjes integral in the last edition? The question is about "The elements of real analysis" by Robert Bartle. In 1st and 2nd editions there are chapters on the Riemann-Stieltjes integral. But in 3rd and 4th editions he replaced it by the Riemann integral.
The reason of the question is the following one : At first I started to study the 2nd edition because I did not know that there are more recent editions. Now I know it. The R.-S. integral is more general than the Riemann integral. So what I must to study?
New editions must be "better". (I think)
So what is the reason for this replacing and is there any need to read old editions?
EDIT: In the introductory chapters in 3rd and 4th editions I did not find the explanation for this.
EDIT: I see that there is an attempt to close this question because someone thinks it is opinion-based. I dont know. I think this question must have resonanle answer. Something like: "There is gauge integral in the reference in the 4th edition. And this integral is more general than R-S integal. R-S is old-fashion now." It is just my fantasy. I want to say that this question must have some meaningfull answer.
 A: I agree with @Masacroso ... Now that measure theory is commonly studied, the Riemann-Stieltjes integral is not needed.
Example: In former times the R-S integral was seen in probability theory.  $$\mathbb{E}[\phi(X)] = \int_{\mathbb{R}}\phi(t)dF(t)$$ where function $F$ is the CDF of the random variable $X$.  Nowadays we write $$\mathbb{E}[\phi(X)] = \int_{\mathbb{R}}\phi(t)d\mu(t)$$ where measure $\mu$ is the distribution of the random variable $X$ in the sense of $\mu(E) := \mathbb{P}(X\in E)$.

There may still be some uses for Stieltjes-type integrals.  But not enough to justify including them in a course that every mathematician takes.
$\bullet\quad$ Stochastic integrals,
$$
\int_0^t X_s\;dY_s
$$
where $(X_s)$ and $(Y_s)$ are semimartingales with respect to a stochastic basis $(\mathcal{F}_s)$.  Defined as a limit (in mean) of Riemann sums.
$\bullet\quad$  The spectral theorem: if $T$ is a self-adjoint operator
on Hilbert space $H$,
$$
T = \int_{\sigma(T)} \lambda\;dE_\lambda
$$
where $\lambda \mapsto E_\lambda$ is a certain nondecreasing family of projections on $H$.  The (measurable) functional calculus is then formulated
$$
\phi(T) = \int_{\sigma(T)} \phi(\lambda)\;dE_\lambda
$$
where $\phi$ is a measurable function defined on $\sigma(T)$.
