Newbetuts

Reconciling measure-theoretic definition of expectation versus expectation defined in elementary probability

$L^{p}$ functions from Rudin Exercises 3.5

Clarification on the meaning of dx in the integral and differential setting

Show that for every set $A \subset \mathbb R^n$ lebesgue measurable $\int_{A} f_n dx\rightarrow \int_{A} f dx.$ [closed]

If $\int_A f\,dm = 0$ for all $A$ having some fixed measure $C$, then $f = 0$ almost everywhere

Lebesgue measure and characterisation of function $\Phi$ [Rudin-Real&Complex]

Yet another definition of Lebesgue integral

Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$

Derivative of $\Gamma(t):=\max_{u\leq t} \int_u^t \gamma \,\mathrm d\lambda$

If $f$ derivable on $[a,b]$ does $\int_a^t f'(x)dx=f(t)-f(a)$ true?

Generalization of Fatou's Lemma

How do I show that the integral of $e^{inx}$ over a set of measure $1$ is nonzero for some nonzero $n$?

Calculating the Lebesgue Integral given only the measure of a set

How do I prove $f=0$ almost everywhere?

If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$

A question about Measurable function

Given a Borel set $B$ prove: for every $\epsilon$, $\exists$ compact and closed sets and a continuous $\phi$...

New posts in lebesgue-integral

$\int_{\mathbb{R}}f(x)e^{-ixz}d\mu_x$ analytic for $f\in L_1$

Definitions of Lebesgue integral

Example of a function in $L^2(\mathbb{R})$ with derivative not in $L^2(\mathbb{R})$.

Reconciling measure-theoretic definition of expectation versus expectation defined in elementary probability

$L^{p}$ functions from Rudin Exercises 3.5

Clarification on the meaning of dx in the integral and differential setting

Show that for every set $A \subset \mathbb R^n$ lebesgue measurable $\int_{A} f_n dx\rightarrow \int_{A} f dx.$ [closed]

If $\int_A f\,dm = 0$ for all $A$ having some fixed measure $C$, then $f = 0$ almost everywhere

Lebesgue measure and characterisation of function $\Phi$ [Rudin-Real&Complex]

Yet another definition of Lebesgue integral

Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$

Derivative of $\Gamma(t):=\max_{u\leq t} \int_u^t \gamma \,\mathrm d\lambda$

If $f$ derivable on $[a,b]$ does $\int_a^t f'(x)dx=f(t)-f(a)$ true?

Generalization of Fatou's Lemma

How do I show that the integral of $e^{inx}$ over a set of measure $1$ is nonzero for some nonzero $n$?

Calculating the Lebesgue Integral given only the measure of a set

How do I prove $f=0$ almost everywhere?

If a sequence $f_n$ is bounded in $L^2$ and converges to zero a.e., then $f_n\to 0$ in $L^p$ for $0<p<2$

A question about Measurable function

Given a Borel set $B$ prove: for every $\epsilon$, $\exists$ compact and closed sets and a continuous $\phi$...