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uniform convergence of integral
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(Definition)
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"uniform convergence of integral" is owned by pahio.
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(view preamble)
Cross-references: number, positive, interval, point, improper integral, real number, domain, continuous, function
This is version 9 of uniform convergence of integral, born on 2004-10-02, modified 2005-07-27.
Object id is 6277, canonical name is UniformConvergenceOfIntegral.
Accessed 4726 times total.
Classification:
| AMS MSC: | 26A42 (Real functions :: Functions of one variable :: Integrals of Riemann, Stieltjes and Lebesgue type) |
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Pending Errata and Addenda
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![$ [c,\,d]$](http://images.planetmath.org:8080/cache/objects/6277/l2h/img7.png "$ [c,\,d]$"){kind=small}
![$ [c,\,d]$](http://images.planetmath.org:8080/cache/objects/6277/l2h/img8.png "$ [c,\,d]$"){kind=small}
![$ x_\varepsilon \in [a,\,b]$](http://images.planetmath.org:8080/cache/objects/6277/l2h/img10.png "$ x_\varepsilon \in [a,\,b]$"){kind=small}
![$\displaystyle \left\vert\int_x^b f(x,\,t)\,dx\right\vert < \varepsilon\quad\forall t\in [c,\,d]$](http://images.planetmath.org:8080/cache/objects/6277/l2h/img11.png "$\displaystyle \left\vert\int_x^b f(x,\,t)\,dx\right\vert < \varepsilon\quad\forall t\in [c,\,d]$")
