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 UnitStep

 http://functions.wolfram.com/14.01.17.0002.01

 Input Form

 UnitStep[x] UnitStep[y] == UnitStep[x y] UnitStep[(x + y)/2] /; Element[y, Reals] && Element[y, Reals]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], " ", RowBox[List["UnitStep", "[", "y", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["x", " ", "y"]], "]"]], " ", RowBox[List["UnitStep", "[", FractionBox[RowBox[List["x", "+", "y"]], "2"], "]"]]]]]], "/;", " ", RowBox[List[RowBox[List["y", "\[Element]", "Reals"]], "\[And]", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]

 MathML Form

 θ UnitStep ( x ) θ UnitStep ( y ) θ UnitStep ( x y ) θ UnitStep ( x + y 2 ) /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] y TagBox["\[DoubleStruckCapitalR]", Function[Reals]] Condition UnitStep x UnitStep y UnitStep x y UnitStep x y 2 -1 x y [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["UnitStep", "[", "x_", "]"]], " ", RowBox[List["UnitStep", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["x", " ", "y"]], "]"]], " ", RowBox[List["UnitStep", "[", FractionBox[RowBox[List["x", "+", "y"]], "2"], "]"]]]], "/;", RowBox[List[RowBox[List["y", "\[Element]", "Reals"]], "&&", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-11-29