Riemann integral oor Fins
Riemann integral
en
A type of integral whose computation involves dividing the interval of integration into smaller sub-intervals, summing sample values of the integrand inside those sub-intervals multiplied by their lengths, and letting the number of sub-intervals tend to infinity.
Vertalings in die woordeboek Engels - Fins
Riemannin integraali
fi
Riemannin integraali ("Riimannin")
Geskatte vertalings
Vertoon algoritmies gegenereerde vertalings
voorbeelde
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Voorbeelde moet herlaai word.
The Riemann–Stieltjes integral, an extension of the Riemann integral.
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In the 19th century, Augustin Cauchy developed epsilon-delta limits, and Bernhard Riemann followed up on this by formalizing what is now called the Riemann integral.
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Around that time, the attempts to refine the theorems of Riemann integration led to the study of the "size" of the set of discontinuities of real functions.
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In the middle of the 19th century Riemann introduced his theory of integration.
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The Riemann integral generalises to the improper Riemann integral to measure functions whose domain of definition is not a closed interval.
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Furthermore, every bounded function on a closed bounded interval has a Lebesgue integral and there are many functions with a Lebesgue integral that have no Riemann integral.
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For functions on the real line, the Henstock integral is an even more general notion of integral (based on Riemann's theory rather than Lebesgue's) that subsumes both Lebesgue integration and improper Riemann integration. However, the Henstock integral depends on specific ordering features of the real line and so does not generalise to allow integration in more general spaces (say, manifolds), while the Lebesgue integral extends to such spaces quite naturally.
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For functions on the real line, the Henstock integral is an even more general notion of integral (based on Riemann's theory rather than Lebesgue's) that subsumes both Lebesgue integration and improper Riemann integration. However, the Henstock integral depends on specific ordering features of the real line and so does not generalise to allow integration in more general spaces (say, manifolds), while the Lebesgue integral extends to such spaces interpolation)
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8 sinne gevind in 4 ms. Hulle kom uit baie bronne en word nie nagegaan nie.