5 supose that mu is a finite bord measure on mathbbr soch that mux0 forall x in mathbbr sypose f

Name: 5 supose that mu is a finite bord measure on mathbbr soch that mux0 forall x in mathbbr sypose f is a borel measmable finction that is integrable unt mu show that gxint inftyx ft d mut is a contimous
Uploaded: 2024-10-23T09:56:03-08:00
Duration: 2 min 14 s
Channel: Shu Naito
Description: 5 supose that mu is a finite bord measure on mathbbr soch that mux0 forall x in mathbbr sypose f is a borel measmable finction that is integrable unt mu show that gxint inftyx ft d mut is a contimous

Question

Scott Stetson · Accepted Answer

Step 1: We need to show that for any x in R and any ε &gt; 0, there exists a δ &gt; 0 such that |G(y)

Question

Suppose that $mu$ is a finite Borel measure on $mathbb{R}$ such that $mu({x})=0, forall x in mathbb{R}$. Suppose $f$ is a Borel measurable function that is integrable wrt $mu$. Show that [ G(x)=int_{-infty}^{x} f(t) d mu(t) ] is a continuous function.

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