English
For families of measure spaces, the canonical Pi-preserving map preserves the product measure across the index set.
Русский
Для семейства мер пространство сохранение произведения по индексу сохраняется для канонического Pi-преобразования.
LaTeX
$$$ \mathrm{MeasurePreserving}\bigl(\mathrm{MeasurableEquiv.pi} (\mu_i) \bigr)\; (\mathrm{Measure.pi}\mu)\; (\mathrm{Measure.pi}\nu) $$$
Lean4
/-- Use as `letI := upgradeStandardBorel α` to endow a standard Borel space `α` with
a compatible Polish topology.
Warning: following this with `borelize α` will cause an error. Instead, one can
rewrite with `eq_borel_upgradeStandardBorel α`.
TODO: fix the corresponding bug in `borelize`. -/
noncomputable def upgradeStandardBorel [MeasurableSpace α] [h : StandardBorelSpace α] : UpgradedStandardBorel α :=
by
choose τ hb hp using h.polish
constructor
