Voltage measurement using the following circuit
240:12V transformer converts the 240Vrms to 12Vrms.

The 3.3K with 12+4.7K is a voltage divider on that which generates ~1.72Vrms across R3.

That's ~+-2.435V peak.

The battery circuit on the right provides a 2.5V reference level which is attached at the top of R3 to fix a reference point. 

Note: Since there is only one connection between the left side and right side, ignoring the scope impedance, that connection simply acts are a reference point. There is no current flowing across that wire.

The scope from the other side of R3 to ground will then show a ~5v peak to peak sinusoidal waveform offset to 2.5V centre.

(Of course, in reality, the scope impedance DOES have an effect and does close a current path connection between left and right. That changes everything a little and Heisenberg pops his head around the corner.)