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It’s use will never result in a posterior distribution which integrates (or sums) to 1. ?

Zaynul Abadin Tuhin
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An improper prior doesn't integrate/sum to 1, hence it is not a proper probability distribution on its own. Depending on the likelihood, the posterior distribution may or may not integrate to one. An example would be a constant function on the infinite line, e.g. $p: \mathbb{R} \rightarrow \mathbb{R}, x\mapsto 1$. It is not normalisable (since its integral is infinite), hence improper, but yet it may serve as an uninformative prior.

Kilroy
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