They are called electromagnetic waves because a light wave is made of a magnetic field which creates an electric field when it collapses, which creates a magnetic field when it collapses, etc.
They can be measured, you can use an antenna and radio to listen to information embedded in radio waves, you can measure the frequency (how quickly it goes from electric to magnetic) and its amplitude (how big the electric fields and magnetic fields are), we can measure its polarisation (the angle of the wave) and its phase (when the electrical fields are strongest as opposed to a when they are strongest in a reference wave)
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