＋ている ［自動詞］落ちる

I just had a sudden, perhaps trivial, realization, yet I am very excited about it.

In the following sentence:

（消しゴムは）机の下に落ちていますよ。

The intransitive verb 落ちる［自動詞］it's being used in the ＋ている form. I read in Japanese Verbs At a Glance [1] that you use this construction only on intransitive verbs in order to express the state of being.

In English you could say The eraser has finished falling under the desk, but only to elicit dumbfounded stares back at you. (The previous sentence would be more plausible in a language evolved in a planet with a very weak gravity.)

I guess The eraser fell under the desk is ok but, correct me if I am wrong, I 'like' The eraser is under the desk. Leaving out the falling part.

How would you translate it?

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[1] Chino, Naoko: (2001). Japanese Verbs at a Glance.

"Intransitive or transitive" is not the indicater of that meaning of ～ている form. The key is whether it is an instantenous/change-of-state verb or not. Indeed, most of instantaneous verbs are intransitive, but still there are transitive verbs whose ～ている form express the current state that results from prior movements, just like 知る, 覚える, 閉じる, 開く, 忘れる, 決める, 借りる, 着る,,,,.

As for the example sentence, it expresses "the eraser fell in the past and the current state of it is under the desk". So "The eraser is under the desk" is a good translation.