Let $A \subseteq \mathbb{R}^n$ be a compact and connected subset of $\mathbb{R}^n$. Suppose that $f:A \rightarrow \mathbb{R}$ is a continuous function and $g:A \rightarrow \mathbb{R}$ an integrable one. Prove that there exists an $x$ such that
$$\int \limits_A f g = f(x) \int \limits_A g $$
Search found 3 matches
- Tue Dec 13, 2016 7:40 pm
- Forum: Real Analysis
- Topic: Existence of $x$
- Replies: 1
- Views: 2564
- Sun Sep 04, 2016 11:15 am
- Forum: Algebraic Structures
- Topic: On Solvable Sylow groups
- Replies: 1
- Views: 2805
On Solvable Sylow groups
Let $p, q$ be prime numbers such that $p<q$ and let $G$ be a group such that $\left| G \right| =pq$.
- Prove that there exists a unique subgroup $H$ such that $\left| H \right| = q$.
- Prove that $H$ is a normal subgroup of $G$.
- Examine if $G$ is a solvable group.
- Sat Aug 27, 2016 4:47 pm
- Forum: Algebraic Structures
- Topic: Groups
- Replies: 1
- Views: 2811
Groups
In $\mathbb{Z}$ we define $a*b=a$ . Prove that $(\mathbb{Z},*)$ isn't a group using the definition.