Measuring device for measuring magnetic properties of the surroundings of the measuring device having a sensor line comprising at least one magnetoresistive sensor element extending in a line direction, which can measure magnetic properties in its surroundings, wherein the sensor element has a width and a length as well as a height, wherein the height is less than the width and the height is less than the length and the line direction points in a direction of the width or in a direction of the length of the sensor element and, with a support field device, which generates a magnetic support field in an area, over which the sensor line extends, and with a pre-magnetization device, having a pre-magnetization magnet or multiple pre-magnetization magnets (6, 7), wherein at least one pre-magnetization magnet (6, 7) is arranged some distance away from the sensor line in a direction that is vertical to the line and that extends in a direction parallel to the line direction, characterized in that - the magnetoresistive sensor element essentially only measures the magnetic properties of the magnetoresistive sensor element's surroundings in one direction designated as a measuring direction of an orthogonal coordinate system or in one plane designated as a sensor measuring plane, spanned by two vertical measuring directions of an orthogonal coordinate system, - with a pre-magnetization device only composed of one pre-magnetization magnet the properties influencing a magnetic field generated by it of the pre-magnetization magnet and its arrangement relative to the sensor line as well as the support field generated by the support field device are selected such that an overlapping magnetic field results from overlapping of the magnetic field and the support field generated by the pre-magnetization device whose strength of the component pointing in the line direction is greater, at least at one location on the sensor line, than the strength of a field component pointing vertically toward the line direction and not in the direction of the height of the sensor element; or - with a pre-magnetization device composed of multiple pre-magnetization magnets (6, 7) the properties, influencing the magnetic field generated by the pre-magnetization magnets (6, 7) and the arrangement of the pre-magnetization magnets (6, 7) relative to the sensor line as well as the support field generated by the support field device are selected such that an overlapping magnetic field results from an overlapping of the magnetic field and the support field generated by the pre-magnetization device whose strength of the field component pointing in the line direction is greater, at least at one location on the sensor line, than the strength of a field component pointing vertically toward the line direction and not in the direction of the height of the sensor element. - the magnetoresistive sensor element essentially only measures the magnetic properties of the magnetoresistive sensor element's surroundings in one direction designated as a measuring direction of an orthogonal coordinate system or in one plane designated as a sensor measuring plane, spanned by two vertical measuring directions of an orthogonal coordinate system, - with a pre-magnetization device only composed of one pre-magnetization magnet the properties influencing a magnetic field generated by it of the pre-magnetization magnet and its arrangement relative to the sensor line as well as the support field generated by the support field device are selected such that an overlapping magnetic field results from overlapping of the magnetic field and the support field generated by the pre-magnetization device whose strength of the component pointing in the line direction is greater, at least at one location on the sensor line, than the strength of a field component pointing vertically toward the line direction and not in the direction of the height of the sensor element; or - with a pre-magnetization device composed of multiple pre-magnetization magnets (6, 7) the properties, influencing the magnetic field generated by the pre-magnetization magnets (6, 7) and the arrangement of the pre-magnetization magnets (6, 7) relative to the sensor line as well as the support field generated by the support field device are selected such that an overlapping magnetic field results from an overlapping of the magnetic field and the support field generated by the pre-magnetization device whose strength of the field component pointing in the line direction is greater, at least at one location on the sensor line, than the strength of a field component pointing vertically toward the line direction and not in the direction of the height of the sensor element.