Newbetuts

$f$ is a non-constant polynomial, $A $ is a set of measure zero, Is this true that $m(f^{-1}A)=0$, where $m$ stands for the Lebesgue measure.

Limit of the absolute value of a function

Why is the Cauchy product of two convergent (but not absolutely) series either convergent or indeterminate (but does not converge to infinity)?

How to prove the Lebesgue density theorem using martingales?

An alternative proof for sum of alternating series evaluates to $\frac{\pi}{4}\sec\left(\frac{a\pi}{4}\right)$

Using Fatou's Lemmas in proving Scheffe's Lemma Part (ii)

Existence of non-constant continuous functions with infinitely many zeros [duplicate]

Why $\lim_{n\to \infty} \frac{(2^2)^{\sqrt n}}{(1+(10)^{-2^2})^n}$ has no limit?

Solve the differential equation $\left(\frac{dy}{dx}\right)^2 [1-2\frac{dy}{dx}y]=c$ where $c\in\Bbb{R}$.

user friendly proof of fundamental theorem of calculus

Find all the functions satisfying $f(x+y)=f(x)+f(y)$ and $f(xy)=f(x)f(y)$ for all real x,y [duplicate]

Prove that there exist linear functionals $L_1, L_2$ on $X$

How to prove the cubic formula without root extraction

Convergence of Riemann sums of a periodic function

How to get the idea of the formula for the mean value property for the heat equation

"Lebesgue" measurabillity on Riemannian manifolds

New posts in real-analysis

Prove that $\lim_{n\to\infty}n^2\int_0^{\frac{1}{n}}x^{x+1}dx=\frac{1}{2}.$

Show that a limit exists

Show that convolution of two measurable functions is well-defined

Rigorous separation of variables.

$f$ is a non-constant polynomial, $A $ is a set of measure zero, Is this true that $m(f^{-1}A)=0$, where $m$ stands for the Lebesgue measure.

Limit of the absolute value of a function

Why is the Cauchy product of two convergent (but not absolutely) series either convergent or indeterminate (but does not converge to infinity)?

How to prove the Lebesgue density theorem using martingales?

An alternative proof for sum of alternating series evaluates to $\frac{\pi}{4}\sec\left(\frac{a\pi}{4}\right)$

Using Fatou's Lemmas in proving Scheffe's Lemma Part (ii)

Existence of non-constant continuous functions with infinitely many zeros [duplicate]

Why $\lim_{n\to \infty} \frac{(2^2)^{\sqrt n}}{(1+(10)^{-2^2})^n}$ has no limit?

Solve the differential equation $\left(\frac{dy}{dx}\right)^2 [1-2\frac{dy}{dx}y]=c$ where $c\in\Bbb{R}$.

user friendly proof of fundamental theorem of calculus

Find all the functions satisfying $f(x+y)=f(x)+f(y)$ and $f(xy)=f(x)f(y)$ for all real x,y [duplicate]

Prove that there exist linear functionals $L_1, L_2$ on $X$

How to prove the cubic formula without root extraction

Convergence of Riemann sums of a periodic function

How to get the idea of the formula for the mean value property for the heat equation

"Lebesgue" measurabillity on Riemannian manifolds