A dual (or single) ramp DVM works by integrating the input voltage over a (usually fixed) period of time. A dual slope DVM then integrates a reference in the opposite direction and measures the time. The voltage measurement is the time divided by the integration period times the reference voltage.
The integral of a fixed voltage is a ramp.
The integral of a sine wave on top of a fixed voltage is a -cosine on top of a ramp (and if the period is chosen to be an integral number of cycles, the effect on the end voltage is nil.
To measure an AC voltage with a slope DVM, the AC voltage is converted to a DC voltage with an RMS to DC converter or a precision rectifier and then measured as above (usually with some scaling factor to give equivalent-to-RMS reading for sinusoidal inputs in the latter case). It is not measured directly.