Newbetuts

Every function on $\mathbb{R}^n$ that is continuous in each variable separately is Borel measurable.

Your Favourite Application of the Birkhoff Ergodic Theorem

Chicken-Egg problem with Fubini’s theorem

Yet another definition of Lebesgue integral

limit of increasing sequence of measures is a measure

Show that a set $D$ is measurable with respect to a product measure $m \times \nu$, (lebesgue $\times$ counting measure)

Existence of a Minimal Cover

Open Measurable Sets Containing All Rational Numbers

Sum of Dirac measures is not regular

Topology and Measures

On a proof of Riesz-Fischer Theorem

Proof of uniqueness of conditional expectation

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

Relax Egoroff's Theorem to pointwise convergence a.e. and bounded a.e. pointwise limit

Proof of a change-of-measure formula

New posts in measure-theory

Confusions about Radon-Nikodym derivative and dominating measures

Product of metric outer measures

For which topological measure spaces do open sets always have positive measure?

Is the integral function of a $L^2[0,1]$ function continuous? [duplicate]

Definition of completion of a measure space

Every function on $\mathbb{R}^n$ that is continuous in each variable separately is Borel measurable.

Your Favourite Application of the Birkhoff Ergodic Theorem

Chicken-Egg problem with Fubini’s theorem

Yet another definition of Lebesgue integral

limit of increasing sequence of measures is a measure

Show that a set $D$ is measurable with respect to a product measure $m \times \nu$, (lebesgue $\times$ counting measure)

Existence of a Minimal Cover

Open Measurable Sets Containing All Rational Numbers

Sum of Dirac measures is not regular

Topology and Measures

On a proof of Riesz-Fischer Theorem

Proof of uniqueness of conditional expectation

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

Relax Egoroff's Theorem to pointwise convergence a.e. and bounded a.e. pointwise limit

Proof of a change-of-measure formula