HP 54710A User's Reference Manual page 234

Measurements
Time-interval measurements
Bandwidth, Sampling Rate, and Reconstruction
The discussion about vertical response told how bandwidth affects
time-interval measurement accuracy. In the HP 54720 oscilloscope, like any
digitizing oscilloscope, the signal is sampled and then quantized by an A/D
converter. In the real-time sampling mode, if the sampling rate is
insufficient, information about the input signal will be lost, just as it would be
if the bandwidth were insufficient.
The Fourier theorem states that complex signals, such as square waves or
triangular waves, can be represented mathematically as the sum of a series of
sine waves. If you know the phase, frequency, and magnitude of every
sinusoidal component, you have all the information about the complex signal.
The Shannon sampling theorem says that if you sample a signal that contains
no frequencies higher than half the sampling rate, all the information about
the signal is contained in the samples. Consider a sine wave with frequency f,
sampled at a rate 2f, as shown in figure 13-22.
Figure 13–22
Sine Wave Having Frequency f and Sampled at Frequency f
13–49