Solution
= Solution
The problem is a <well-posed Bayesian inverse problem in total variation> when a unique posterior $\mu^y$ exists for every $y\in Y$ and the posterior map is continuous:
$$
y_n\longrightarrow y
\quad\Longrightarrow\quad
d_{\mathrm{TV}}(\mu^{y_n},\mu^y)\longrightarrow0.
$$
Thus the metric supplies the precise meaning of continuous dependence on the observed data in the Bayesian version of <Hadamard well-posedness>.