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Question: Is this set compact? If yes, how can I prove it?

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#real-analysis #general-topology #functional-analysis #partial-differential-equations
60
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Uniform convergence of a series depending on $\alpha ,\beta$

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#real-analysis #sequences-and-series #uniform-convergence
65
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Determining the sign of an integral using the mean value theorem.

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#calculus #real-analysis #integration #definite-integrals
472
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Understanding theorem 9.12 in Rudin's PMA

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#real-analysis #analysis
89
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Show that $S={\bigcup \limits_{n=1}^{\infty} \left(n - \frac{1}{n}, n + \frac{1}{n}\right)}$ cannot be a union of open balls of radius $r$

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#real-analysis #metric-spaces
90
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Is $\mathbb{P}(S_n/n>p+a)$ a decreasing function of n?

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#real-analysis #probability #probability-distributions
703
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Prove that if $f$ is strictly increasing at each point of (a,b), then $f$ is strictly increasing on (a,b).

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#real-analysis #proof-writing #epsilon-delta
36
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If $f(x)=3x^y, y∈N$ what should the value be for $y$ so that their is a maxima or minima at $x=0$?

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#calculus #real-analysis #derivatives
32
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(Proof Correction): Suppose $f: [0,1] \rightarrow [0,1]$ which is cont. diff. and $|f'(x)| \leq 1/2$, then it has unique fixed point.

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#real-analysis
107
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compact convex sets

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#real-analysis #convex-analysis
17.6k
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Is a Lipschitz function differentiable?

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#calculus #real-analysis #analysis #derivatives #lipschitz-functions
479
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Show that $F$ is a $\pi$-system.

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#real-analysis #measure-theory
150
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Analysis Counterexamples

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#real-analysis #convergence-divergence #examples-counterexamples #uniform-convergence #sequence-of-function
93
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What does "x <= y or not" mean?

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#real-analysis #elementary-set-theory
855
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Understanding extended Riemann integral in Munkres.

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#real-analysis #multivariable-calculus #improper-integrals #riemann-integration

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