# Questions tagged [stieltjes-integral]

For questions about Stieltjes integrals. Use with other tags as needed, such as [riemann-integration], to specify Riemann–Stieltjes, Lebesgue–Stieltjes, etc.

181 questions
Filter by
Sorted by
Tagged with
98 views
+50

### A question on integrating a function, with respect to another function?

I've been asked to find the area described by $$A={ (x,y), y^2 \leqslant2x; and, y\geqslant 4x-1 }$$ which is effectively the following area(If I can insert a graph using mathJax, please let me ...
1 vote
56 views

### How does this theorem on continued fractions relate to the Riemann-Stieltjes integral?

I'm going to include two precursor sections here to introduce all of the content referenced in my actual question (if you're familiar with both continued fractions and the Riemann-Stieltjes integral, ...
• 2,612
27 views

• 53
1 vote
Let $0=t_0<t_1<\cdots<t_n=T$ be a partition of the interval $[0,T]$. Denote $\Delta t_k\equiv t_{k+1}-t_k$ for every $0\leq k<n$. Assume $\lim_{n\to\infty}\Delta t_k=0$. Find the limit of $... • 1,494 0 votes 1 answer 68 views ### Calculate$\sup_{f \in \mathcal{F}} \int_{-1}^1 f dg$for$g=x^2$. The following is from Bruckner's Real Analysis book (Ex.12:8.3): Let$g(x)=x^2$on$[−1, 1]$, and let$\mathcal{F} = {\{f \in \mathcal{C}[−1,1] : |f(x)| ≤ 5 \ \text{for all} \ x∈[−1,1]}\}$. Calculate ... 0 votes 1 answer 72 views ### Show that$|\int_a^b f dg | \le \|f\|_{\infty} \|g\|\$ 