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In this small note we explicit the relation between Ito and Stratonovichintegrals when conditional measure flow components are present in theintegrands. The `correction' term involves Lions-type measure derivatives andclarifies which cross-correlations need to be taken into account. We cast theframework in relation to SDEs of mean-field type depending on conditional flowsof measure. The result being trivial under full flows of measure.

On the relation between Stratonovich and Ito integrals with functional integrands of conditional measure flows