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We show uniqueness in law for a general class of stochastic differential equations in <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="double-struck">R</mi> <mi>d</mi> </msup> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>d</mi> <mo>≥</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula>, with possibly degenerate and/or fully discontinuous locally bounded coefficients among all weak solutions that spend zero time at the points of degeneracy of the dispersion matrix. Points of degeneracy have a <i>d</i>-dimensional Lebesgue–Borel measure zero. Weak existence is obtained for a more general, but not necessarily locally bounded drift coefficient.