To provide an acid-type sulfonic acid group-containing polymer which is excellent in hydrogen gas barrier properties and hot water resistance and which generates less oligomer during production; a liquid composition and a polymer electrolyte membrane comprising this acid-type sulfonic acid group-containing polymer; and a membrane electrode assembly and a polymer electrolyte fuel cell provided with the polymer electrolyte membrane.;This acid-type sulfonic acid group-containing polymer is a polymer which has perfluoromonomer units, no monomer units having a halogen atom other than a fluorine atom, and acid-type sulfonic acid groups, and of which the hydrogen gas permeability coefficient under the conditions of a temperature of 80° C. and a relative humidity of 10%, is at most 2.5×10−9 cm3·cm/(s·cm2·cmHg), and the mass reduction rate when being immersed in hot water at 120° C. for 24 hours is at most 15 mass %, wherein the TQ value of a polymer having fluorosulfonyl groups which is a precursor of the polymer having acid-type sulfonic acid groups, is at least 220° C.
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