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Prove a sequence of functions has a subsequence converging to $L^1$

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#real-analysis #convergence-divergence #solution-verification #sequence-of-function
78
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What's the function before $f_0(x)$ in Fast-growing Hierarchy

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#calculus #sequence-of-function
110
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Sequences and Greatest Integer Function

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#sequences-and-series #weak-convergence #ceiling-and-floor-functions #sequence-of-function
58
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For $f(x)=-x^3$ the sequence $f^n(x)$ converges to $0$

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#real-analysis #sequences-and-series #dynamical-systems #sequence-of-function
46
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Showing that a sequence of functions is monotonically increasing

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#real-analysis #sequence-of-function
28
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On switching order of differentiation and infinite summation

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#real-analysis #derivatives #sequence-of-function
245
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Doubt on uniform convergence and sup-metric convergence

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#metric-spaces #uniform-convergence #cauchy-sequences #sequence-of-function
96
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Is pointwise limit of random variable a random variable?

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#probability-theory #random-variables #sequence-of-function
38
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Supremum of a very simple sequence of functions

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#real-analysis #supremum-and-infimum #sequence-of-function
256
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If a sequence of functions converges pointwise, then the supremum converges?

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#real-analysis #sequence-of-function
144
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A Monotone Uniformly Convergent Sequence for a Bounded Function (Bartle's Exercise 2L)

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#real-analysis #measure-theory #measurable-functions #sequence-of-function
1.5k
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Sequence of continuous functions on $[0,1]$ pointwise converging to an unbounded function

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#continuity #examples-counterexamples #sequence-of-function #pointwise-convergence
67
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Sequence of function which converges pointwise, is it also uniform?

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#sequences-and-series #uniform-convergence #sequence-of-function
59
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Sequence of right differentiable functions

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#real-analysis #functional-analysis #sequence-of-function
72
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If $0\leq f_{n}\leq g_{n}$, $f_{n}\longrightarrow f$, $g_{n}\longrightarrow g$, $\int_{0}^{1}g{n}\longrightarrow \int_{0}^{1}g$, then so is $f_{n}$.

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#measure-theory #lebesgue-integral #lebesgue-measure #measurable-functions #sequence-of-function

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