  Exchangeability concerning a continuous exposure, X, may be assumed to
identify average exposure effects of X, AEE(X). When X is measured with error
(Xep), three challenges arise. First, exchangeability regarding Xep does not
equal exchangeability regarding X. Second, the non-differential error
assumption (NDEA) could be overly stringent in practice. Third, a definition of
exchangeability that implies that AEE(Xep) can differ from AEE(X) is lacking.
To address them, this article proposes unifying exchangeability and
exposure/confounder measurement errors with three novel concepts. The first,
Probabilistic Exchangeability (PE) is an exchangeability assumption that allows
for the difference between AEE(Xep) and AEE(X). The second concept, Emergent
Pseudo Confounding (EPC), describes the bias introduced by exposure measurement
error through mechanisms like confounding mechanisms. The third, Emergent
Confounding, describes when bias due to confounder measurement error arises. PE
requires adjustment for E(P)C, which can be performed like confounding
adjustment. Under PE, the coefficient of determination (R2) in the regression
of Xep against X may sometimes be sufficient to measure the difference between
AEE(Xep) and AEE(X) in risk difference and ratio scales. This paper provides
comprehensive insight into when AEE(Xep) is a surrogate of AEE(X). Differential
errors could be addressed and may not compromise causal inference
