Given a sigma algebra $ mathcal {F} $ on a tray $ X $. Let's be even more sigma ideal $ I $ https://en.wikipedia.org/wiki/Sigma-ideal. Then we can consider $ mathcal {F} / I = {[A] mid A in mathcal {F} } $ or $ [A] = {A triangle Z mid Z in mathcal {F} } $.

is $ mathcal {F} / I $ still a sigma algebra? And a sigma algebra on which set, on [X]?