There is no datasheet in post #3 but is datasheet in post #4 for HA which is different series, HF (OP's one) just don't exist in the nature (except aliexpress). But even if we are taking HA series, yes it says: "Designed specifically for horizontal deflection current correction of TV's where high frequencies and high ripple currents are applied. "
I didn't say that the spec sheet was referenced in post #3; I said it was referenced in reply #3. Look just below the subject line of each post after the first--the reply # is there.
The OP seemed to think that the linked spec sheet might be relevant to the application for this cap even though it isn't the spec for the HF series. He says the cap goes in a 30 year old CRT. Apparently the HF series is obsolete, and probably was used to carry currents at the horizontal frequency of a CRT; the designation HF might have stood for "high frequency". I searched for a spec for a Nichicon HF series, but couldn't find one.
Other evidence that this cap is intended to carry currents at frequencies substantially higher than 120 Hz is its physical size and its low ESR.
A typical 10 uF, 50V electrolytic is nowhere near this big, and the ESR for this cap is around .1 ohm, more or less, in the vicinity of 10s of kilohertz. If the cap is carrying 3 amps, for example, the dissipation in the cap would be around 1 watt. A more typical 10 uF electrolytic has an ESR of several ohms.
The large physical size of this cap allows it to dissipate 1 watt without any problem.
However if you would read datasheet a little bit more carefully:
"Capacitance Tolerance ±10% at 120Hz, 20°C"
I read it carefully enough to see that the spec is, strictly speaking, for the HA series, not the HF series.
If we could find an actual spec sheet for the HF series, it might specify the capacitance at 15.75 kHz, or even higher. That would make sense, since they obviously used heavily etched foil to make this cap. Perhaps the HA series didn't use etched foil, and its capacitance doesn't vary 2 to 1 as the measurement frequency increases toward the SRF.
As I said above, even though the spec sheet is for the HA series, the description of a capacitor designed to carry horizontal frequency currents would seem to be applicable, even if perhaps not exact in every respect.
You seem to be missing the point of my post. The point I was making is that if the Nichicon cap is intended to operate at frequencies above 10 kHz, the capacitance at those frequencies is what we care about, and it's nearer to 10 uF than it is to 20 uF. The capacitance measured by a DVM (they effectively measure at a very low frequency), or by an LCR meter at 120 Hz is not really relevant to use of the capacitor at horizontal deflection frequencies. The capacitance marked on the cap is correct if the measurement is made at a much higher frequency than 120 Hz.
The OP wondered why his meter gives a value of about 20 uF when the value marked on the cap itself is 10 uF. I gave him an explanation.