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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

0 votes
1 answer
312 views

Deduce that a function is zero on interval $[0,M]$

I have been thinking about this for the last few days but I was not able to produce a definitive answer. Take an integrable function $g$ that maps in $\mathbb{R}$ and with domain contained in $[0,M]$ …
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1 answer
239 views

Riemann-Liouville integral of $f$ is zero implies $f =0$ a.e

The Riemann-Liouville integral is defined by $$ I^\alpha f(x)=\frac{1}{\Gamma(\alpha)} \int_a^x f(t)(x-t)^{\alpha-1} d t $$ where $\Gamma$ is the gamma function and $a$ is an arbitrary but fixed base …
Grandes Jorasses's user avatar