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Supply is major source of noise in bandgap's .With already placed bypass caps at supplies ,high frequency noise is already gets filtered ,what might get coupled at output is low frequency supply noise .Measuring PSR at 100Khz or even little more would be good enough .
The internal noise from the BGR is more of a trouble compared to Supply noise.
Read thesis by Holman for low noise BGR.
In that he mentions depending on the noise from BGR could you only decide the application it could be used for. example the resolution in ADC decides the BGR noise
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