[morzh]

Well,

your pot is connected between Antenna and GND with its end pins.
If you disconnect the pot's middle pin from antenna transformer primary coil, the resistance between these end pins will be the pot's listed value, 20K, or whatever it is today after wear, maybe 30K. If you have a crack in the pir's resistive element, then you will measure infinite, or very high (in Megaohms) resistance.

Pot's wiper slides along the resistive element, and is connected to the middle pin, and so if you measure between it and any end pin while rotating the shaft (this moving the wiper) you will see the resistance changed from very low (Ohms, maybe tens of Ohms) to the full scale (20 kOhm or, again, maybe 30kOhm if it is worn).
If it is cracked, then you will see the resistance change and then, when you pass the crack, jump up to that very high value.

Now what can be happening in your case, IF you indeed see the infinity on your meter (seeing zero in the Low position is wrong) and 40 ohm or so in Full position this may mean your pot is cracked, otherwise you's see that 40 ohm going gradually to 20 kOhm.


Now. Since at the Full position you do get 40 or so, you have contact there.
So, have you tried the antenna reception at Full position?
Depending where the crack is (if it is) you might lose reception at the very top, or close to the bottom.


So.

1. Connect your DMM between A and GND, and note the resistance at FULL (clockwise all the way).
2. Slowly rotate the volume CCW, see if it jumps to Zero or Infinity (very high) and notice the place where it happens.
3. If it indeedgoes to zero......your pot ends are swapped and your CW position is Min Vol, and CCW is Max Vol.