Why is an improbable early universe unacceptable?

[spacejunkie]

Please define what a measure problem is.

A measure problem is either when different measures applied to the same space in a theory produce different predictions or there is no way to define a measure on a space at all.

Measures in set theory and topology are ways to assign numbers to subsets. They generalise lengths, areas and volumes.

https://en.wikipedia.org/wiki/Measure_(mathematics)

Measures also apply to probability spaces so come into topics like entropy and quantum theory.

Measure problems are endemic in cosmological theories and many different regularisation procedures have been created to overcome them but none are generally accepted. In eternal inflation theories the problem is how to apply probability measures to infinite sets of causally disconnected universes. In canonical quantum gravity the Wheeler-deWitt equation is regularisation dependent.

https://en.wikipedia.org/wiki/Measure_problem_(cosmology)

Please define what a measure problem is.