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Limits Involving $e$ - Is this acceptable?

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#real-analysis #limits
125
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Suppose $f$, $g$ are positive continuous functions on $[a,\infty)$ for some $a\in \mathbb{R}$, and $\int_a^{\infty}g(x) \,\mathrm{d}x$ diverges

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#real-analysis
26
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proof $\{a_n\}$ is bounded (check)

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#real-analysis #sequences-and-series
34
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Prove that the set $S$ is equal to the set of all Liouville numbers

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#real-analysis #measure-theory #liouville-numbers
138
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Exchanging the limit and integral can be restricted to smaller measurable sets

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#real-analysis
440
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Exercise 4.13 from Rudin, what's wrong with this proof.

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#real-analysis #metric-spaces #continuity #uniform-continuity
59
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The infimum of the given set

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#real-analysis #supremum-and-infimum
673
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Integrating the following function

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#real-analysis #integration #lebesgue-measure
2.6k
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How to check a function is positive definite?

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#real-analysis #probability-theory #fourier-analysis #fourier-transform #characteristic-functions
181
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how to Prove $τ=\inf\{t:B(t)=\max\limits_{0<s<1}B(s)\}$ is a random variable?where B(t) is brownian motion process

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#real-analysis #functional-analysis #measure-theory #stochastic-calculus #stopping-times
58
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pointwise convergence with integrals

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#real-analysis
114
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How to show that $f$ is monotone?

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#real-analysis
34
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What is the technique to determine $\sum_{n=1}^{\infty} M_n$ if the given series of function is a trigonometric series with $n$ as power?

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#real-analysis #uniform-convergence
64
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Show that $J_0(x)=\sum\limits_0^\infty \frac{(-1)^n x^{2n}}{4^n(n!)^2}$ is $J_0(x)=\frac{1}{\pi}\int_0^\pi \cos(x\sin\theta)d\theta$

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#real-analysis #integration #power-series #taylor-expansion
84
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Showing a function grows like a certain power of $n$

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#real-analysis #limits

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