Κοιτάω τα εισερχόμενά μου κάθε πρωί, αλλά σήμερα δεν έχει έρθει κανένα καινούριο email.

Here it means I check / I look at.

With things like email, messages, or a phone screen, κοιτάω often means to check in a very natural way:

• Κοιτάω τα εισερχόμενά μου = I check my inbox

A learner should also know that κοιτάω and κοιτάζω are both correct. They mean the same thing:

• Κοιτάω
• Κοιτάζω

Both are very common in Modern Greek.

Τα εισερχόμενα is the usual Greek way to say inbox or incoming mail/messages.

Literally, it means something like the incoming ones/things. It is plural because Greek often treats this idea as a set of incoming messages, not as a single box.

So:

• τα εισερχόμενα = the inbox / incoming messages
• τα εισερχόμενά μου = my inbox

In real usage, this is a standard computer/email expression.

That extra accent appears because μου is an enclitic word, meaning it leans on the previous word.

The base form is:

• εισερχόμενα

But when an enclitic like μου follows a word with stress far enough from the end, Greek often adds a second written accent:

• εισερχόμενά μου

This helps show the correct stress pattern.

So the extra accent is not random; it is a regular spelling rule with enclitics such as:

• μου
• σου
• του
• της
• μας
• σας
• τους

In Greek, weak possessive forms like μου usually come after the noun:

• το βιβλίο μου = my book
• ο φίλος μου = my friend
• τα εισερχόμενά μου = my inbox

This is the normal pattern.

English uses:

• my inbox

Greek usually uses:

• the inbox my → τα εισερχόμενά μου

Greek can also use stronger possessive wording in special cases, but for everyday possession, noun + μου/σου/του... is the standard structure.

Because κάθε normally goes directly with the noun, without an article:

• κάθε μέρα = every day
• κάθε εβδομάδα = every week
• κάθε πρωί = every morning

So:

• κάθε πρωί is correct
• κάθε το πρωί is not standard Greek

Also notice that κάθε is followed by a singular noun even though the meaning is repeated or habitual:

• κάθε πρωί = every morning

Because Greek does not need a dummy subject like English there.

English says:

• There hasn’t arrived any new email
• more naturally, No new email has arrived

Greek simply says:

• δεν έχει έρθει κανένα καινούριο email

The real subject is κανένα καινούριο email, and Greek can place it after the verb very naturally.

So Greek does not need an extra word equivalent to English there in this kind of sentence.

Δεν έχει έρθει is the perfect form, similar to English has not come / has not arrived.

It suggests a result that is still relevant now:

• today, up to this moment, no new email has arrived

That fits very well with σήμερα because today is still an ongoing time period.

By contrast:

• δεν ήρθε = it didn’t come / arrive This is more like a simple past event.

So in this sentence:

• σήμερα δεν έχει έρθει κανένα καινούριο email means something like
• today, no new email has arrived so far

That is because έρχομαι is an irregular verb.

Important forms are:

• dictionary form: έρχομαι = I come
• aorist: ήρθα = I came
• perfect: έχω έρθει = I have come

So έρθει is the form used with έχω to make the perfect:

• έχει έρθει = has come / has arrived

This is one of those verbs whose forms need to be learned as a family, because they are not all built in an obvious way from the present stem.

Yes, from an English point of view it looks like a double negative, but in Greek this is normal and correct.

Greek commonly uses negative concord, which means the negative particle and the negative-type word appear together:

• δεν είδα κανέναν = I didn’t see anyone
• δεν έχω τίποτα = I don’t have anything
• δεν έχει έρθει κανένα email = no email has arrived / there hasn’t been any email

So δεν ... κανένα is standard Greek, not bad grammar.

In English, you usually choose one negative form:

• I didn’t see anyone not
• I didn’t see no one

But Greek works differently.

Because email is usually treated as a neuter singular noun in Greek:

• το email

So the words agreeing with it must also be neuter singular:

• κανένα = neuter singular
• καινούριο = neuter singular

That gives:

• κανένα καινούριο email = no new email / no new e-mail

Also, there is no article here because κανένα already functions as the determiner.

Yes. Both mean new.

You will see both:

• καινούριο
• καινούργιο

They are just variant forms of the same adjective. In this sentence, καινούριο email and καινούργιο email both work.

The full adjective is:

• masculine: καινούριος / καινούργιος
• feminine: καινούρια / καινούργια
• neuter: καινούριο / καινούργιο

So the sentence uses the neuter singular because of email.

Yes. That is very common in modern everyday Greek.

Greek often keeps international tech words in Latin script, especially in casual writing:

• email
• site
• link
• chat

You may also sometimes see Greek spellings of some loanwords in other contexts, but email in Latin letters is extremely normal.

Even though it stays in Latin letters, Greek still treats it grammatically like a Greek noun:

• το email
• κανένα email
• πολλά email

You could, but the meaning shifts a little.

• email specifically means email
• μήνυμα means message, which is broader

So:

• κανένα καινούριο email = no new email
• κανένα καινούριο μήνυμα = no new message

If you specifically mean the inbox of your email account, email is the more precise choice here.