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New posts in uniform-convergence
Consider $g_n(x)= \sqrt{x^2+1/n}$ for $x \in [-1,1]$ and $n$ be a natural number. Find the limit $g(x)$ of $g_n(x)$. Is the convergence uniform? [duplicate]
real-analysis
sequences-and-series
convergence-divergence
uniform-convergence
Compare the topology of pointwise convergence with the vector topology in the space of the continuous scalar functions $C(I)$
general-topology
functional-analysis
examples-counterexamples
uniform-convergence
topological-vector-spaces
The sequence $n\sin(\sqrt{4\pi^2n^2 +x^2})$ converges on compacts:
real-analysis
sequences-and-series
limits
solution-verification
uniform-convergence
Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence
real-analysis
proof-writing
uniform-convergence
lipschitz-functions
sequence-of-function
the space of continuous functions is complete
real-analysis
proof-writing
metric-spaces
uniform-convergence
If $|h(x,t)|\leq g(t)$ then the integral $f(x) = \int_a^{\infty} h(x,t)dt$ is uniformly convergent.
real-analysis
integration
uniform-convergence
Dini's Theorem. Uniform convergence and Bolzano Weierstrass.
sequences-and-series
convergence-divergence
continuity
uniform-convergence
Theorems similar to Dini's Theorem and Egoroff's Theorem
real-analysis
measure-theory
reference-request
uniform-convergence
pointwise-convergence
Show uniform convergence of bounded functions implies uniform boundness.
real-analysis
sequences-and-series
convergence-divergence
uniform-convergence
Uniform convergence of a parametric integral. Which solution is correct?
improper-integrals
uniform-convergence
$f_n$ uniformly converge to $f$ and $g_n$ uniformly converge to $g$ then $f_n \cdot g_n$ uniformly converge to $f\cdot g$
real-analysis
analysis
convergence-divergence
uniform-convergence
Is there integrable function sequence which is uniformly converges to not integrable function?
integration
uniform-convergence
Examine the uniform convergence of $\sum_{n=1}^{\infty} \frac{x}{(1+nx)(1+(n+1)x)}$
real-analysis
sequences-and-series
uniform-convergence
sequence-of-function
Uniform Convergence of $\langle f_n \rangle = (nx)/(1+n^3x^2)$ for $0 \leq x \leq 1$
real-analysis
uniform-convergence
is uniform convergent sequence leads to bounded function?
uniform-convergence
bounded-variation
Uniform limit of uniformly continuous functions
real-analysis
analysis
uniform-convergence
uniform-continuity
convergence-divergence
Uniform convergence and weak convergence
real-analysis
probability-theory
uniform-convergence
weak-convergence
Exponential function and uniform convergence of polynomials.
real-analysis
sequences-and-series
exponential-function
uniform-convergence
Is a power series uniformly convergent in its interval of convergence?
calculus
real-analysis
power-series
uniform-convergence
$\sum_{n=1}^\infty\frac{z^n}{n}$ does not converge uniformly on $\mathbb{D}$.
sequences-and-series
complex-analysis
power-series
uniform-convergence
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