Intereting Posts

Math Subject GRE 1268 Question 55
$g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
If H ≤ Z(G) ≤ G, where G is a finite group,Z(G) is its center, and (G:H) = p for some prime p, then G is abelian.
if $A$ has Lebesgue outer measure $0$ then so does $B=\left\{x^2: x\in A \right\}$
Intuitive explanation of a definition of the Fisher information
A difficult integral evaluation problem
Integral using Parseval's Theorem
How to plot a phase portrait for this system of differential equations?
Summation Theorem how to get formula for exponent greater than 3
Are Monotone functions Borel Measurable?
“8 Dice arranged as a Cube” Face-Sum Equals 14 Problem
Representation theory over $\mathbb{Q}$
If $(f\circ g)(x)=x$ does $(g\circ f)(x)=x$?
Are all algebraic integers with absolute value 1 roots of unity?
A Question on Probability – Hunter and Rabbit

In general, I know that it is not necessarily the case that the product of two Lebesgue integrable functions $f,g$ will be Lebesgue integrable. But I was reading in a textbook that if at least one of these functions is bounded, then their product will be Lebesgue integrable. How can we prove this statement? I’d appreciate some input on this, thanks.

- How do we prove that $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$?
- Intuition behind the ILATE rule
- Asymmetric Hessian matrix
- Is this proof sufficient to show that a concave function of a metric is also a metric?
- Show that $f(x)=||x||^p, p\ge 1$ is convex function on $\mathbb{R}^n$
- Distance to a closed set
- Continuous function that attain local extrema every point
- Is $\int_{M_{n}(\mathbb{R})} e^{-A^{2}}d\mu$ a convergent integral?
- Showing a set is closed in $\mathbb R^2$
- Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$

If $|f|\le M$ almost everywhere, then $|fg|\le M|g|$ almost everywhere hence $\displaystyle\int|fg|\le M\int|g|$ is finite because $g$ is integrable.

- To show inverse of tan x
- Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^22^n}$
- Matrix exponential of a skew symmetric matrix
- Goat tethered in a circular pen
- Number of relations that are both symmetric and reflexive
- Elements of finite order in $SL_2(\mathbb{Z})$
- Any more cyclic quintics?
- Intuition about infinite sums
- How do I show that a holomorphic function which satisfies this bound on reciprocals of integers is identically zero?
- Diophantine equations solved using algebraic numbers?
- Primes congruent to 1 mod 6
- I'm having trouble with a proof by induction
- How many combinations of $3$ natural numbers are there that add up to $30$?
- Property of critical point when the Hessian is degenerate
- $E \subset \mathbb R$ is an Interval $\iff E$ Is connected