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Uniform and absolutely convergence of functions

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#sequence-of-function
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Interchanging limit and supremum

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#limits #inequality #supremum-and-infimum #sequence-of-function
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Example of a sequence $(f_n)_n$, such that $(f_ n')_n$ converges uniformly, but $(f_n)_n$ doesn't converge in any point.

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#real-analysis #sequences-and-series #examples-counterexamples #uniform-convergence #sequence-of-function
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Sequence of Measurable Functions Converging Pointwise

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#real-analysis #sequences-and-series #measure-theory #sequence-of-function
659
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Prove that the limit of a sequence of polynomials a polynomial

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#real-analysis #functional-analysis #sequence-of-function
69
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Sequence of uniform convergent sequence $\{f_n\}$ such that $\{f_n'\}$ does not converge

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#real-analysis #continuity #sequence-of-function
433
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Suppose $f_n : [0,1]\rightarrow\mathbb{R}$ is a sequence of $C^1$ functions that converges pointwise to $f$.

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#real-analysis #sequence-of-function
74
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Continuity of limit on a compact set implies uniform convergence

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#continuity #uniform-convergence #sequence-of-function
34
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Show that $f_n (x)$ converges to $f(x)=0 \ \forall x$

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#pointwise-convergence #sequence-of-function
421
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Let $X$ be a metric space with metric $d$.Then $d:X \times X\rightarrow \mathbb R$ is continuous?

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#real-analysis #proof-verification #metric-spaces #continuity #sequence-of-function
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Convergence in measure iff every subsequence has a convergant subsequence

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#real-analysis #measure-theory #sequence-of-function
366
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Relation between uniform convergence and derivatives

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#uniform-convergence #sequence-of-function
27
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$F$ normal in $H(\Omega) \iff$ normal in $U$

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#complex-analysis #convergence-divergence #sequence-of-function
221
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Calculate $\lim_{n\to\infty}\int_0^1\frac{nx}{1+n^2 x^3}\,dx$.

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#real-analysis #sequences-and-series #lebesgue-integral #sequence-of-function
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Is this entrance exam question correct regarding uniform convergence?

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#real-analysis #sequences-and-series #contest-math #uniform-convergence #sequence-of-function

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