Let's say $f$ and $g$ are „nice enough” to $$\sum_{k}f\left(\xi_{k}\right)\left(g\left(x_{k+1}\right)-g\left(x_{k}\right)\right)\rightarrow\int_{a}^{b}f\left(x\right)dg\left(x\right),$$ where $\xi_{k}\in\left[x_{k},x_{k+1}\right]$, $a\leq x_{0}\leq x_{1}\leq\ldots\leq x_{n}\leq b$, but how do we interpret the convergence above? In what sense does it converge?
2026-03-26 14:34:25.1774535665
What is the „limit type” in the definition of Stieltjes-integral?
40 Views Asked by user129445 https://math.techqa.club/user/user129445/detail AtRelated Questions in REAL-ANALYSIS
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