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Characteristic function converges pointwise to 0 - Baby Rudin

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#real-analysis #convergence-divergence #sequence-of-function
70
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Pointwise limit of seq.

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#real-analysis #calculus #sequences-and-series #convergence-divergence #sequence-of-function
75
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Big–O for sequence with multiple indices

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#sequences-and-series #convergence-divergence #asymptotics #sequence-of-function
125
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Investigate convergence of a sequence of functions $(f_n)_{n \in \mathbb{N}}$ with $ f_n(x)= \frac{x^{2n}}{1+x^{2n}}$

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#uniform-convergence #sequence-of-function #pointwise-convergence
383
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Limit function of Taylor series of $x\ln(x)$

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#real-analysis #solution-verification #taylor-expansion #sequence-of-function
26
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Convergence of the sequence $\frac{1}{nx}$ in $\mathbb{B}(0,1)$

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#metric-spaces #complete-spaces #sequence-of-function
49
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Question on integration/differentiation of function series

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#real-analysis #integration #sequences-and-series #sequence-of-function
115
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Pointwise and uniform convergence of $f_n(x)=\sqrt[n]{nx^2+1}$

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#solution-verification #uniform-convergence #sequence-of-function
49
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Uniform boundness question

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#real-analysis #functional-analysis #uniform-convergence #sequence-of-function
1.7k
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If $f_n\to f$ pointwise on $\mathbb{R}$ and each $f_n$ is bounded, then $f$ is bounded (counter-example) + question on uniform convergence proof

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#real-analysis #examples-counterexamples #uniform-convergence #sequence-of-function #pointwise-convergence
200
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Counter examples on uniform convergence

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#real-analysis #proof-writing #examples-counterexamples #uniform-convergence #sequence-of-function
63
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Let $f_n\to f$ pointwise on a set $E$. If $|f_n(x)-f(x)|\le a_n \ \forall x\in E$ with $a_n\to 0$, then the convergence is uniform

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#real-analysis #functions #proof-writing #uniform-convergence #sequence-of-function
55
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Uniform convergence of $(f_n)_{n \in \Bbb{N}}$ on $D_1 \cup D_2$

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#real-analysis #solution-verification #uniform-convergence #sequence-of-function
365
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Boundedness of a sequence of bounded, measurable functions on a closed subset of a finite-measure set

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#real-analysis #measure-theory #lebesgue-measure #sequence-of-function #measurable-functions
42
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Example of a sequence that follows certain properties

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#real-analysis #functional-analysis #lp-spaces #sequence-of-function

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