To answer your first questions sequentially:

1.) Redshift is a term used to describe the displacement of spectral lines in the light emitted by objects in the universe, caused by the Doppler effect. It is a measure of how much the universe has expanded since the light was emitted by the object. In astronomy, redshift is used to determine the distance of an object from Earth.

2.) In the context of the abstract, the redshift range refers to the distance of the galaxies being studied, with 𝑧  6 􀀀 9 indicating that the galaxies are very far away from Earth, with a redshift of 6 to 9. This range corresponds to a time period in the early universe, when galaxies were just starting to form and evolve.

3.) The range of 𝑧  6 􀀀 9 is interesting because it allows us to study the properties of galaxies during this early period of the universe's history. The use of strong gravitational lensing also allows us to observe fainter and smaller galaxies than in blank fields, providing a more complete picture of the galaxy population during this time.

4.) In general, size and luminosity are positively correlated for galaxies, meaning that larger galaxies tend to be more luminous. However, there may be some exceptions to this trend, such as with dwarf galaxies, which are relatively small but can be quite luminous due to their high star formation rates. It is also possible for a galaxy to have an unusually high or low luminosity for its size, due to factors such as mergers or black hole activity. However, in the context of the abstract, the focus is on the overall trend of the size-luminosity relation for galaxies within the given redshift range.
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