real analysis related issues & queries in MathXchanger

If a continuous function $f: U \to \mathbb R$, $U$ open, has compact support, then f is Riemann integrable on $U$. What's $\tilde f$ an extension of?

real-analysis calculus integration measure-theory differential-geometry
Updated April 26, 2019 12:20 PM

A compactly supported continuous function on an open subset of $\mathbb R^n$ is Riemann integrable. What is the relevance of openness in the proof?

real-analysis calculus integration measure-theory differential-geometry
Updated April 26, 2019 12:20 PM

Problem explanation regarding subspaces of $\mathbb{R}$

definition real-numbers retraction
Updated April 26, 2019 12:20 PM

Disjointed balles.

real-analysis general-topology
Updated April 26, 2019 11:20 AM

Showing that the limits the same

sequences-and-series limits analysis
Updated April 26, 2019 11:20 AM

(n-1) derivative in residue theorem

complex-analysis
Updated April 26, 2019 11:20 AM

Tyrtyshnikov's proof that polynomial roots depend continuously on the coefficients

analysis polynomials proof-explanation equicontinuity
Updated April 26, 2019 11:20 AM

Big O /Right or wrong?

real-analysis asymptotics
Updated April 26, 2019 11:20 AM

Find sequence limit $x_{n+1} = \frac{3}{4} x_n + \frac{1}{4} \int_0^{|x_n|} f(x) dx$

real-analysis sequences-and-series limits analysis
Updated April 26, 2019 08:20 AM

Baby Rudin 2.17

real-analysis general-topology proof-verification
Updated April 26, 2019 08:20 AM

Can I define a closed subset in a normed vector space as below?

real-analysis linear-algebra general-topology elementary-set-theory numerical-methods
Updated April 26, 2019 06:20 AM

Tempered Distribution Convolve with Approximate Identity

functional-analysis distribution-theory
Updated April 26, 2019 06:20 AM

Is there an example of an analytic function whose derivative is not analytic?

real-analysis
Updated April 26, 2019 06:20 AM

Reference for proof of theorem on directional derivative

multivariable-calculus reference-request vector-analysis
Updated April 26, 2019 06:20 AM

Proving properties of $\exp(x)$

real-analysis
Updated April 26, 2019 04:20 AM

Limit Points and Differentiability

real-analysis general-topology
Updated April 26, 2019 04:20 AM

Uniformly continuous and bounded set.

real-analysis
Updated April 26, 2019 04:20 AM

Why are these two characterizations of compact operators equivalent?

general-topology functional-analysis hilbert-spaces banach-spaces compact-operators
Updated April 26, 2019 04:20 AM

Show that the graph of a convex function is above any tangent plane

measure-theory convex-analysis
Updated April 26, 2019 04:20 AM

Relationship Between Fourier Cosine/Sine Transforms and Fourier Transforms

calculus proof-verification fourier-analysis
Updated April 26, 2019 03:20 AM

There are no other clopen sets in $\mathbb{R}$ except for $\mathbb{R}$ and $\emptyset$

real-analysis general-topology proof-verification real-numbers connectedness
Updated April 25, 2019 23:20 PM

Approximating the integral of an $L^1$ function by the integral over a finite set.

real-analysis measure-theory
Updated April 25, 2019 23:20 PM

Differentiability and integrability of a function composed with itself

real-analysis derivatives riemann-integration
Updated April 25, 2019 23:20 PM

Suppose $\dot{x}=Ax$, A in $\mathbb{R}^{2\times2}$. Determine A, using data.

real-analysis linear-algebra systems-of-equations dynamical-systems
Updated April 25, 2019 22:20 PM

Riemann Zeta function with a twist

calculus complex-analysis number-theory summation riemann-zeta
Updated April 25, 2019 22:20 PM

Half of proof to show rational numbers are dense in the reals

real-analysis
Updated April 25, 2019 22:20 PM

Prove that $\limsup_{x\to\infty}\left(\cos x + \sin\left(\sqrt2 x\right)\right) = 2$

real-analysis calculus limits trigonometry limsup-and-liminf
Updated April 25, 2019 22:20 PM

Residues for a Laurent series with two centres

complex-analysis laurent-series
Updated April 25, 2019 19:20 PM

Slightly alternative proof to the converse part of Cauchy's General Principle

real-analysis proof-verification convergence cauchy-sequences limsup-and-liminf
Updated April 25, 2019 17:20 PM

Joukowsky transformation of function that has complex conjugate

complex-analysis mathematical-physics fluid-dynamics
Updated April 25, 2019 17:20 PM

Error in the Chudnovsky Formula

complex-analysis numerical-methods asymptotics
Updated April 25, 2019 17:20 PM

If the value of the determinant $\begin{vmatrix} a & 1 & 1\\ 1 & b & 1\\ 1 & 1 & c \end{vmatrix} > 0 $ then prove that $abc> -8$

determinant matrix-equations matrix-analysis
Updated April 25, 2019 16:20 PM

Question in Volterra operator

functional-analysis
Updated April 25, 2019 16:20 PM

Prove the given normed space is not a Banach space

real-analysis functional-analysis banach-spaces
Updated April 25, 2019 15:20 PM

Interpolation between log and polynomials using Riesz-Thorin

functional-analysis analysis operator-theory interpolation interpolation-theory
Updated April 25, 2019 15:20 PM

Integrate 2-Form Along Loop to get 1-Form?

vector-analysis differential-forms
Updated April 25, 2019 15:20 PM

Stronger version of finite additivity of Legesgue measure

real-analysis analysis measure-theory lebesgue-measure
Updated April 25, 2019 15:20 PM

Integral and norm

real-analysis multivariable-calculus normed-spaces
Updated April 25, 2019 15:20 PM

Show that a closed graph and compact codomain implies continuity.

functional-analysis analysis metric-spaces compactness
Updated April 25, 2019 13:20 PM

Show that $\lim \inf x_n$ is an adherence value

real-analysis sequences-and-series proof-verification limsup-and-liminf
Updated April 25, 2019 13:20 PM

Proving an inequality which contains exponentials

real-analysis inequality
Updated April 25, 2019 13:20 PM

Prove that $T$ is not contraction and $T^2$ is contraction

functional-analysis fixed-point-theorems
Updated April 25, 2019 13:20 PM

Solutions of second order ordinarydifferential equation

real-analysis ordinary-differential-equations pde
Updated April 25, 2019 12:20 PM

Taking a limit of a function defined by an integral

real-analysis limits
Updated April 25, 2019 12:20 PM

Trouble understanding limit of a sequence of complex numbers, James Brown

sequences-and-series complex-analysis limits limits-without-lhopital
Updated April 25, 2019 11:20 AM

$\{ a + b\sqrt{2} \ : \ a, b \in \mathbb{Z} \}$ dense in $\mathbb{R}$?

real-analysis real-numbers
Updated April 25, 2019 10:20 AM

How do you show $\frac{\epsilon \sin(\epsilon t)}{1-\epsilon t } = \mathcal{O(\epsilon ^2)} \quad (1 \leq t \leq 1000)$

real-analysis limits
Updated April 25, 2019 10:20 AM

Ununderstood estimating of $|f({3\over 4})|$

complex-analysis
Updated April 25, 2019 10:20 AM

All accumulation values of sequence

real-analysis sequences-and-series limits analysis
Updated April 25, 2019 10:20 AM

Does the function $f(x) = \sum_{n=1}^\infty P(|X_n| > x)$ have any special properties?

real-analysis analysis probability-theory measure-theory terminology
Updated April 25, 2019 10:20 AM

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