Darboux integral

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Calculus
Integral
Interval
Mathematics
Real analysis
Riemann integral
Function

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Published in Hugo D. Junghenn, Principles of Analysis, 2018

Hugo D. Junghenn

A bounded function f:[a,b]→R $ f:[\boldsymbol{a},\boldsymbol{b}] \rightarrow \mathbb R $ is Darboux integrable iff it is Riemann integrable. In this case, R(f)=∫abf $ R(f) = \int _{\boldsymbol{a}}^{\boldsymbol{b}} f $ .

⋄_α-Measurability and combined measure theory on time scales

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Published in Applicable Analysis, 2022

Chao Wang, Guangzhou Qin, Ravi P. Agarwal, Donal O'Regan

f is said to be -integrable from a to b if . Then, we write for this common value and call this integral, the Darboux -integral.

Darboux integral

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Integration

⋄α-Measurability and combined measure theory on time scales

⋄_α-Measurability and combined measure theory on time scales