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You can test capacitors with an ohmmeter. A good capacitor behaves like a short circuit when you first apply a voltage, then its resistance increases as it charges. The capacitors that fail are electrolytic types with polarity, so be sure to put the meter ground lead on the capacitor negative. The cap will be marked. An open capacitor will show no kick in the reading, and a shorted cap will show a constant low resistance.

Now, having said all that, ohming a capacitor isn't 100% effective as a test. A capacitor's value may change to the point where a circuit will stop working, but if the cap isn't shorted or completely open, or is just a very low value, the ohmmeter test won't show a problem. A capacitance tester is better. Many digital meters include a capacitance test function.

Most inverter circuits have only a small number of capacitors, and it's usually faster just to change them all. If you replace a capacitor, keep the capacitance the same (the microfarad value) but use a little higher voltage rating. Caps come in standard voltage values, and they get physically larger as the rating increases, but if you just go up one level the new part will usually fit. The main reason these go bad is that the manufacturer used too low a voltage to begin with. It keeps costs down, but the parts are stressed and often can't deal with it.