Histone demethylase that specifically demethylates 'Lys-4' of histone H3, thereby playing a central role in histone code. Does not demethylate histone H3 'Lys-9', H3 'Lys-27', H3 'Lys-36', H3 'Lys-79' or H4 'Lys-20'. Demethylates trimethylated and dimethylated but not monomethylated H3 'Lys-4'. May play a role in spermatogenesis. Involved in transcriptional repression of diverse metastasis-associated genes; in this function seems to cooperate with ZMYND8. Suppresses prostate cancer cell invasion. Regulates androgen receptor (AR) transcriptional activity by demethylating H3K4me3 active transcription marks (By similarity). 3 2-oxoglutarate + N(6),N(6),N(6)-trimethyl-L-lysyl(4)-[histone H3] + 3 O2 = 3 CO2 + 3 formaldehyde + L-lysyl(4)-[histone H3] + 3 succinate Binds 1 Fe(2+) ion per subunit. Interacts withPCGF6, MSH5, ZMYND8, AR. The JmjC domain is required for enzymatic activity. Belongs to the JARID1 histone demethylase family.