Let ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\operatorname {P} )} be a probability space on which two sub σ-algebras G 1 ⊆ G 2 ⊆ F {\displaystyle {\mathcal {G}}_{1}\subseteq {\mathcal {G}}_{2}\subseteq {\mathcal {F}}} are defined. For a random variable X {\displaystyle X} on such a space, the smoothing law states that if E ⁡ [ X ] {\displaystyle \operatorname {E} [X]} is defined, i.e. min ( E ⁡ [ X + ] , E ⁡ [ X − ] ) < ∞ {\displaystyle \min(\operatorname {E} [X_{+}],\operatorname {E} [X_{-}])<\infty } , then