sadixon49 is technically right, but the peak observed on a typical multimeter or onboad ammeter would still probably be about 2x-3x. An oscilloscope would show more, if measuring the true peak, but it goes by so fast nothing in a typical RV or residential circuit has time to react to it. For an RV a/c compressor, the peak lasts about 1 second (maybe 1.5 or even 2), and the value seen on a display or inexpensive VOM will be an average over something like 0.25 seconds.
The inverter sees this peak as well, and tries to draw the DC amps needed to sustain it. If the a/c draws 30A/120v during start-up (mine is measured at 28-33A, depending on line voltage), then the inverter attempts to pull about 310-360A from the battery bank. That much current draw sends the battery voltage plummeting, usually far enough to cause the inverter to trip out on a low voltage fault. With a big enough battery bank, however, the voltage may stay within an acceptable range. "Big enough" is probably upwards of 800AH, but it depends on temperature, cable sizes, battery condition, etc. as well as the actual battery rating. Even after the start-up surge (which occurs every time the compressor cycles on), the continuous amp draw is on the order of 130+ amps. which probably requires a battery bank rated for something like 4x-5x that, even to provide power for just an hour.
There is a lot of "Kentucky windage" and assumptions in the above estimates, but it gives an idea of what it takes to start and run an a/c compressor on an inverter.