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TauCeti.RepresentationTheory.SU2.Borel

The Borel structure of SU(2) #

SU(2) carries the subspace topology of the 2 × 2 complex matrices, which makes it a compact Hausdorff topological group (TauCeti/RepresentationTheory/SU2/Basic.lean), but no measurable structure comes with it. This file equips it with its Borel σ-algebra, which is what lets the Haar measure of a compact group -- and with it the theory of TauCeti/RepresentationTheory/Compact/ -- be applied to SU(2).

The σ-algebra is taken to be borel SU(2) by definition, so the MeasurableSpace and BorelSpace instances agree by construction and no compatibility lemma is needed.

@[instance_reducible]

SU(2) carries its Borel σ-algebra, the measurable structure Haar measure needs.

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