Can the expansion of matter in the form of stars and galaxies in the infinite space be considered as an expansion of the infinite universe?

Let's clear up a few misconceptions first: Matter itself is not expanding - *space* is. Space is an actual *thing*, and it can and does expand. Matter is just along for the ride.

If space is expanding, how come you're not expanding with it? A complex web of electromagnetic forces holds your molecules close together and prevents them from being carried apart as space expands. For larger objects, gravity is also a major factor. Stars in our galaxy are prevented from expanding away from each other by gravity. Even nearby galaxies are held close by gravity. But for distant galaxies, the rate of expansion between us and them is so great that they are being carried away from us faster than our mutual gravitational attraction can pull us together. You see, the more space there is between two points, the more *expansion* there is between those points.

While nobody knows for sure that the Universe is infinite, we *do* know that the Universe is flat to within a very small margin of error. A flat Universe is consistent with an infinite Universe. There is no positive evidence to suggest that the Universe is closed (which would imply a finite Universe).

Contrary to some peoples' assertions, an infinite Universe need not be solid. An infinite Universe also does not negate the Big Bang theory; it just forces us to reevaluate how we think about it.

Regardless of the overall size of the Universe, we can only see a finite portion of it. The Universe is 13.8 billion years old. Many people naively think that we can only see things that are closer than 13.8 billion light years away, but this ignores the fact that the Universe has been perpetually expanding since its birth. Consequently, we can actually "see" out to a radius of about 46 billion light years. Beyond that is the so-called Cosmic Microwave Background radiation, left over from an event called Recombination that happened about 380,000 years after the Big Bang.

I hope that answers your question. Good luck!

EDIT: I'll try to redirect my answer to better address your question.

How do we measure the expansion of space? Obviously we cannot "see" space-time itself, but we can see objects that are being carried away from us *by* space-time. We can see distant galaxies, particularly galaxies that host quasars, and there are complicated equations that allow us to calculate the distance to a quasar based on its brightness and redshift. The redshift also tells us how fast a quasar is moving. When we look out into the Universe and we see that (A) all distant galaxies are moving away from us and (B) the further a galaxy is, the faster it appears to be moving - that's pretty strong evidence that space itself is expanding...and we know about how fast space is expanding. Space is expanding at a rate of about 70 kilometers per second per Megaparsec. In other words, for ever Megaparsec of space (3.26 million light years or 31 quintillion kilometers) between two points, those points are moving apart at 70 kilometers per second. If the points are *two* Megaparsecs apart, then they are mutually receding at 140 km/s, and so on.

Let me try to answer the question from a theoretical basis with regards to the expansion of an infinite space.

General Relativty is what is used as the basis for theoretical models of the universe. There is a cosmological solution of general relativity, based on certain simplifying assumptions, that can be used to explain the expansion of the universe and whether space is infinite or finite.

An important preliminary point is the underlying geometric model of General Relativity. It describes space-time as something called a (pseudo) Riemann manifold. This is a fancy way of saying that space-time is fully described by the intrinsic geometry of the manifold and does not need the universe to be embedded in any higher dimensional space. The expansion is simply the expansion of the intrinsic metric and it doesn't matter whether space is infinite or finite - the theory doesn't care. So, general relativity allows the expansion of an infinite universe.

From the cosmological solution of general relativity, you can determine the possible geometries of the universe based on on observed expansion rates, average energy density and pressure density of the universe, etc. One of the possible geometries is a universe that is flat on the cosmological scale. All measurements we have done indicates that the universe is indeed flat. From the metric of a flat universe, we can determine that the universe would have no upper bound on the distance between any two points. This means the universe would be infinite if flat. And since the expansion is intrinsic, it can be infinite and expanding.

There is one caveat. There are topologies which would allow the universe to be flat but finite. We have no reason to expect though that these topologies exist, although it would be satisfying if they did since we could have a flat universe consistent with observation but finite.

It's not the matter in the universe expanding. It's space itself expanding. Think of space like a balloon - As you blow up the balloon, the mass does not actually change, but the balloon expands. And that's what's happening with the universe.

Yes.

The universe is essentially infinite and it is expanding.

The distant parts of the universe are receding from us at near to the speed of light.

And because space itself is expanding ... it is thought that there are galaxies beyond what we can see, that are receding from us faster than the speed of light.

If so we can never reach those galaxies and the universe is essentially infinite..

Space is not infinite and the Universe is not infinite.

Matter is not expanding either. So apart from those three basic errors I should explain thst a finite Universe is expanding at an increasing rate.