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Cesaro-Stolz limit

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#real-analysis #sequences-and-series #limits #recurrence-relations
1.1k
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Does any bounded set $A$ have bounded boundary $\partial A$?

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#real-analysis #general-topology #metric-spaces
907
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Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$

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#real-analysis #inequality #proof-explanation #ceiling-and-floor-functions
54
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Determine the following limits

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#real-analysis #sequences-and-series #limits
2.3k
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Decreasing and bounded below sequence

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#real-analysis #sequences-and-series
44
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Bounded sequences.

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#real-analysis #sequences-and-series
32
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Asymptotic for $\sum_{k \in \mathbb{Z} }\frac{1}{(a|k|+b)^{1+c}} $

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#real-analysis #sequences-and-series #asymptotics
113
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Functional equation $f(x-F(x))=f(x)$

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#real-analysis #integration #functional-equations
143
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Retrospective sequence

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#real-analysis #sequences-and-series
92
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A question on relating Riemann-Stieltjes integral and Lebesgue integral

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#real-analysis #measure-theory #lebesgue-integral
35
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Find the supremum and infimum of this set

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#real-analysis #proof-verification #supremum-and-infimum
10.6k
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Prove that if $f$ and $g$ are continuous functions then $f/g$ is also continuous

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#real-analysis #continuity
255
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If $f''(x)$ exist in $(a, b)$ then there exist $\xi \in (a, b)$ so that $f''(\xi)(b-a)=f'(b)-f'(a)$

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#real-analysis #derivatives
494
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Mean value of a convex function

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#real-analysis #integration
94
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What class of functions $f:\mathbb R\to\mathbb R$ are s.t. every point is a Lebesgue point?

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#real-analysis #functional-analysis #measure-theory

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