Even the righteousness of God through faith of Jesus Christ unto all (and upon all is added in the Textus Receptus, but ill supported) them that believe: for there is no distinction. We observe that the expression here used is not ἡ διὰ πίστεως but simply διὰ πίστεως.
Thus διὰ πίστεως does not naturally connect itself with δικαιοσύνη θεοῦ as defining it, but rather with εἰς πάντας which follows, and perhaps with reference to the πεφανέρωται of Romans 3:21 understood.
The idea, then, may be still that of God's own righteousness, manifested in Christ, unto or towards all believers, who through faith apprehended it and became sharers in it. When St. Paul elsewhere speaks of the believer's imputed righteousness, his language is different, so as to make his meaning plain.
Thus Romans 4:6, ᾧ ὁ θεὸς λογίζεται δικαιοσύνην δικαιοσύνης πίστεως; Romans 5:17, τῆς δωρεᾶς τῆς δικαιοσύνης; Romans 9:30 δικαιοσύνην τὴν ἐκ πίτσεως; Philippians 3:9, τὴν ἐκ θεοῦ δικαιοσύνην ἐπὶ τῇ πίστει.
What we contend for is simply this—that the phrase δικαιοσύνη θεοῦ means God's own righteousness, which, manifested in the atoning Christ, embraces believers, so that to them too righteousness may be imputed (Romans 4:11).