New answers tagged integration
8
votes
When are the chirp signals orthogonal?
just for the record, the distance function has a complicated expression in terms of the imaginary error function erfi:
$$d(x,y)=2T+\operatorname{Re}\,\left\{(\alpha+\alpha')^{-1/2}(-1)^{3/4} \left[\...
- 172k
7
votes
Accepted
If $f$ is a derivative and $f=g$ a.e. for some Riemman integrable function $g$, then can we obtain the Riemann integrability of $f$?
Since $f$ is equal a.e. to $g$, $f$ is Lebesgue integrable. Now for $a < x < y < b$,
$$F(y) - F(x) = \int_x^y f(t)\; dt = \int_x^y g(t)\; dt$$
(see e.g. Rudin, Real and Complex Analysis, ...
- 53.2k
8
votes
Accepted
Are “most” bounded derivatives not Riemann integrable?
In 1977 Clifford E. Weil showed that $A$ is a first Baire category set (i.e. a meager set) in $X$ (sup norm) -- see The space of bounded derivatives. So the situation, at least with respect to one ...
- 3,097
1
vote
Accepted
Average distance between points of lower dimensional simplices in $\mathbb R^n$
It is highly unlikely that an explicit expression exists.
Even the calculation of the volume of a polytope is a nontrivial problem, solved by Lawrence for simple polytopes. One can possibly use ...
- 110k
5
votes
Accepted
On the Riemannian integrability of the bounded derivative
The answer to the question in the body of your post is no, for the reason that if $f' = g$ almost every where and $g$ is Riemann integrable and such that (*) holds, then $f'$ must be Riemann ...
- 35.3k
3
votes
Accepted
Can we integrate arbitrary rational functions of Jacobian elliptic functions?
The answer is positive. Rational function of Jacobi elliptic function is elliptic, and for every elliptic function $f$,
$f(z)dz$ is an Abelian differential, and integral of it is an Abelian integral. ...
- 87.1k
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