Eugene Wigner, On unitary representations of the inhomogeneous Lorentz group, Annals of Mathematics, 40 (1939) 149–204

The observation that Wigner’s representations $U_{(-)}$ are those for which all the maps $g \mapsto \langle \Phi \vert U_g \Psi \rangle$ are measurable and their correspondence of irreducible unitary representations to induced representations of irreps of the stabilizer group of a given momentum is (e.g. Dragon 16) due to

George Mackey, Induced Representations of Groups and Quantum Mechanics, W. A. Benjamin, New York, 1968

Review includes

Bert Schroer, Wigner Representation Theory of the Poincaré

Group, Localization, Statistics and the S-Matrix_, 1996 (pdf)