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We present a natural and simple proof of the Radon - Nikodym theorem formeasures with values in the space of bounded linear operators on a separableHilbert space. This space is not separable, that is why it is essential toassume in the theorem that the range of the measure is separable. We alsodiscuss distinctions between uniform and strong operator measures (Remark 3.3to Lemma 3.2, Theorem 3.5 and its Corollary 3.6).  Proof of this version of the Radon - Nikodym theorem either is not presentedin known literature, or given for special cases and with some inaccuracies (seeComment at the end of the paper), or given in too general form (e. g.,Bourbaki) and uses notations that make it hard to apply the theorem.

On special cases of Radon - Nikodym theorem for vector and operator valued measures