New posts in real-analysis

Does $f'$ analytic imply $f$ analytic?

calculus real-analysis analyticity

Does the implicit function theorem imply Peano existence theorem

real-analysis functional-analysis ordinary-differential-equations calculus-of-variations implicit-function-theorem

Problem involving maximum and minimum of a continuous function

real-analysis analysis

Convergence of $\sum_{n=1}^{\infty}\frac{1}{3^n\ \sin(n)}$

real-analysis sequences-and-series

An interesting series $\sum_{n=2}^{\infty} \sum_{k=0}^{\infty} \frac{1}{(2k+3)^n-1}$

calculus real-analysis sequences-and-series

0 to the power of 0, what does the essential discontinuity actually look like?

calculus real-analysis visualization

Is $\mathbb{Z}= \{\dots -3, -2, -1, 0 ,1 ,2 , 3, \dots \}$ countable?

real-analysis elementary-set-theory

Separation in compact spaces

real-analysis general-topology proof-verification continuity

Example of distinctions between multiple integral and iterated integrals.

calculus real-analysis integration multivariable-calculus riemann-integration

An interesting integral with log: $\int_{0}^{\pi/2}\ln^2\left(\tan^2\left({x\over 2}\right)\right)\mathrm dx=\frac{\pi^3}2$ [closed]

real-analysis integration definite-integrals closed-form

Haar measure - a problem from Folland

real-analysis measure-theory topological-groups

One Question about the Fubini's Theorem

calculus real-analysis integration multivariable-calculus

Prove sum of the lengths of intervals in a finite covering of $\mathbb{Q}\cap [0,1]$ is $\geq 1$

real-analysis measure-theory proof-verification lebesgue-measure

Proofs of $\cos(x+y) = \cos x\cos y - \sin x \sin y$

real-analysis trigonometry

Absolute value of functions in Sobolev space

real-analysis partial-differential-equations sobolev-spaces

$\sigma$-algebra of sets that are both $G_\delta$ and $F_\sigma$

real-analysis general-topology probability-theory measure-theory

Euler Transform elementary Proof

real-analysis numerical-methods power-series

Parallelogram / Polarization Inequality

real-analysis functional-analysis multivariable-calculus inequality hilbert-spaces

Showing that g is integrable and $\int^b_a{f}$ = $\int^b_a{g}$

real-analysis partitions-for-integration

Showing that Sobolev norms on manifolds are equivalent

real-analysis functional-analysis differential-geometry differential-topology sobolev-spaces