The invention relates to a measuring device for measuring the magnetic properties of the surroundings of the measuring device by means of a sensor line having at least one magnetoresistive sensor element extending in a line direction, which can measure the magnetic properties in the surroundings thereof, wherein the sensor element has a width and a length as well as a height, wherein the height is smaller than the width, and the height is smaller than the length, and the line direction points in the direction of the width or in the direction of the length of the sensor element, and having a support field device which generates a magnetic support field in the area over which the sensor line extends, having a premagnetization device which comprises a premagnetization magnet or several premagnetization magnets, wherein at least one premagnetization magnet is arranged in a direction which is perpendicular to the line direction, spaced from the sensor line, and extends in a direction parallel to the line direction, characterized in that magnetoresistive sensor element can measure the magnetic properties of the surroundings thereof substantially in only one direction, referred to as the measurement direction, of an orthogonal coordinate system, or substantially in only one plane, referred to as the sensor measurement plane, which is defined by two perpendicular measurement directions of an orthogonal coordinate system, in that, in the case of a premagnetization device which consists of only one premagnetization magnet, the properties of the premagnetization magnet, which influence the magnetic field generated by said magnet and the arrangement of said magnet relative to the sensor cell as well as the support field generated by the support field device are selected in such a manner that an overlap magnetic field forms due to the overlap of the magnetic field generated by the premagnetization device and of the support field, wherein the strength of the field component of said overlap magnetic field, which points in the line direction is, at least at one site on the sensor line, greater than the strength of the field component which is perpendicular to the line direction and does not point in the direction of the height of the sensor element, or in the case of a premagnetization device consisting of several premagnetization magnets, the properties of the premagnetization magnet, which influence the magnetic field generated by said magnets, and the arrangement of the premagnetization magnets relative to the sensor cell as well as the support field generated by the support field device are selected in such a manner that an overlap magnetic field forms due to the overlap of the magnetic field generated by the premagnetization device and of the support field, wherein the strength of the field component of said overlap magnetic field, which points in the line direction is, at least at one site on the sensor line, greater than the strength of the field component which is perpendicular to the line direction and does not point in the direction of the height of the sensor element.