δικαιοσύνης [2 verses](noun sg fem gen) "Righteousness" is from dikaiosune, which means "righteousness", "justice", "fulfillment of the law," "being in an ideal state." And the "business of a judge. -- This word is only used here and two verses after this. It is related to another Greek word that has almost the same meaning as another word, but that word has the sense of fulfilling social requirements, while this is fulfilling the job of a judge.

δικαιοσύνην, [10 verses](noun sg fem acc) "Righteousness" is dikaiosyne, which means "righteousness", "justice", "fulfillment of the law," and "the business of a judge." It carries the sense of virtue but specifically that of fulfilling legal or social requirements. -- The word translated as "righteousness" also means "justice" and generally "fulfillment of the law". When applied to God or any judge, it works best as "justice," but when applied to people "virtue" or "law-abiding" works better since we don't use "righteousness" must anymore.

δίκτυον,  [2 verse](noun sg neut acc) "Nets" is from diktyon, which means "fishing net", "hunting net", and "lattice work".

διωγμοῦ [3 verses](noun sg masc gen) "Persecution" is diogmos, which means "the chase," "pursuit," and "harassment." Related to the much more common dioko.  -  - "Persecution" is from a noun which means "the chase," "pursuit," and "harassment."

διώξετε [12 verses](verb 2nd pl fut ind act) "Persecuted" is dioko, which means "to cause to run," "to set into motion," "to pursue," "to chase [away]," to follow," "to seek after," "to be hurried (passive)," "to urge on," "to prosecute [legally]," " or "to drive." -- The word translated as "persecute" means "to chase" in both the sense of "chase away" and "seek after." It also means "to prosecute' in a legal sense. Jesus usually uses it in the negative sense of "hounding" someone but in one verse, Luke 17:23, Jesus uses it in the positive sense of following a leader.  In English, we describe someone as being chased and harassed as "being hounded." That idea seems to come closest to capturing Jesus's use of this word.