How do the balls maximizing the maximal function depend on their centers?

Let $ \mu$ be a finite Borel measure on $ \mathbb R^N$ and let $ f\in L^1(\mu)$ be a non-negative function. Let $ M_\mu f$ denote the maximal function of $ f$ relative to $ \mu$ , i.e. $ (M_\mu f)(x)=0$ if $ \mu(B(x,r))=0$ for some $ r>0$ and $ (M_\mu f)(x) = \sup_{0<r<\infty} \frac{1}{\mu(B(x,r))} \int_{B(x,r)}f \, d\mu$ otherwise. (Here $ B(x,r)$ denotes the open ball of radius $ r$ centered at $ x$ .)

Suppose that $ a>0$ and $ K\subset \mathbb R^N$ is a compact such that $ M_\mu f > a$ on $ K$ . Then for each $ x\in K$ there exists $ r_x>0$ such that $ $ \frac{1}{\mu(B(x,r_x))} \int_{B(x,r_x)}f \, d\mu > a. \tag{1}$ $

Question. Is it possible to choose for each $ x\in K$ the radius $ r_x>0$ in such a way that (1) holds and the mapping $ x\mapsto r_x$ is continuous or at least Borel?

This question is inspired by another recent question about Besicovich type covering theorem.

UK visa Application Support Centers biometric appointments suspended; Does anyone have a screenshot of VFS Global’s website from an earlier update?

Today, 4/15/2019, I went to my scheduled biometrics appointment where I received the same slip of paper shown in a previous question: Why are UK visa biometrics appointments suspended at USCIS Application Support Centers?

One answer to that question quoted from the VFS Global website:

If you are an affected customer and have missed your appointment due to this service interruption, you may present at your chosen ASC location on a ‘walk-in’ basis, as soon as you see the message on this page that service has been restored.

However, the VFS Global website currently doesn’t mention this bit about a ‘walk-in’ basis once the problem clears up. Does anyone have a screenshot of this earlier update? My stage 1 visa endorsement letter is only good for three months, two and a half months have already passed, and my worry is that even if this issue does clear up before my letter expires, I’ll have to reschedule a biometrics appointment and with the backlog of applicants, the earliest possible appointment time may be well after my letter expires. My hope is that with this evidence, I may indeed walk-in at my appointed ASC location even if VFS Global later decides to do reschedulings rather than take walk-ins. I realize it’s quite a long-shot.

Also, any update on the why these services have been suspended?

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