Let μ and ν be fixed probability measures on a filtered space (varOmega, F, allowbreak(Ft )t Î R+ )(varOmega, mathcal{F}, allowbreak(mathcal{F}_{t} )_{tin mathbf{R}^{+} } ). Denote by μ T and ν T (respectively, μ T− and ν T−) the restrictions of the measures μ and ν on FTmathcal{F}_{T} (respectively, on FT-mathcal{F}_{T-} ) for a stopping time T. We find the Hahn decomposition of μ T and ν T using the Hahn decomposition of the measures μ, ν and the Hellinger process h t in the strict sense of order frac12frac{1}{2}. The norm of the absolutely continuous component of μ T− with respect to ν T− is computed in terms of density processes and Hellinger integrals.
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机译：令μ和ν为已过滤空间（varOmega，F，allowbreak（F t ） tÎR + ）（varOmega ，mathcal {F}，allowbreak（mathcal {F} _ {t}）_ {tin mathbf {R} ^ {+}}）。用μ T 和ν T （分别为μ T-和ν T-）表示在F T mathcal {F} _ {T}（分别在F T- mathcal {F} _ {T-}）上测量μ和ν的停止时间T.我们使用度量μ，ν的Hahn分解和Hellinger过程h t 找出μ T 和ν T 的Hahn分解从严格意义上讲，是frac12frac {1} {2}。 μ T-的绝对连续分量相对于ν T-的范数是根据密度过程和Hellinger积分计算的。
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