hello,
average of the signal is its DC, since it is LPF it passes DC and other Low frequency components and blocks the high ones (i.e.makes average).
u can just make simple LPF with a cap. and resistor and find the transfer function , then just get the limits at extreme frequencies.
Maybe, you can think about it.
In Fourier analysis, the dc component of a periodic waveform is equal to its average value.
You can use a LPF to pass the dc term of a signal and reject its higher terms.
A low pass filter can the dc term means that it can get the average value of signal.